Inspiron 3847, add graphic card with 2 or 3 HDMI/Display Port?

Intel 4600 Graphics is on the CPU chip, it's not a separate card. So you can certainly install an add-in video card in the PCI-e x16 slot (#19 in motherboard photo on page 11).

You only have a 300W power supply in this PC, so that limits what cards you can use.  You also need to know if your PSU has a direct PCI-e power cable connection for the video card, or not, which will further limit your choices. (Service Manual doesn't say, but I doubt PSU has the extra PCI-e power connector.)

Dell validated these video cards in Inspiron 3847:

• NVIDIA GeForce GT 625
• NVIDIA GeForce GT 635
• NVIDIA GeForce GT 705

You're not limited to these cards, as long as the one you choose has a recommended PSU rating of 300W (or less) and if -or not- it requires the PCI-e power connection.  See if you can find one with the number and type of ports you need.

As for whether you can use both the onboard Intel Graphics port and a port on the video card at same time, you may need to look in BIOS setup to see if it has an option for Multi-Display (or similar) and enable it. If not, your 4th Gen CPU probably only allows use of the Intel port when there's no add-in video installed.

Here's a different option: Get a USB3>HDMI (or >DP) dongle. Connect the dongle to one of the rear USB3 ports on PC and connect dongle to a cable to the monitor.  Just make sure the dongle supports your version of Windows and the "recommended" (aka: "native" or "optimal") resolution of the monitor connected to the dongle. This should let you use the onboard Intel port for 1st monitor and the dongle for a second one at same time...

@RoHe​ Hello, when I googled them, they only have 1 HDMI port, I need graphic card that have (2) HDMI ports to connect to my Dell Monitor U2415.   I tried USB3 dongle, but it didn't work well.
1) Can I use  "DVI to HDMI/DisplayPort" cable?
2) Is NVDIA Quadro NVS310 (2 HDMI port) compatible with Inspiron 3847?
3) Do you have other recommendation? 

Thank you for your help

NVIDIA GeForce GT 625 has 1 HDMI, 1 DVI
NVIDIA GeForce GT 635 has 1 HDMI, 1 DVI, 1 VGA
NVIDIA GeForce GT 705 has 1 HDMI, 1 DVI, 1 VGA

You could use either a DVI(PC)>HDMI(monitor) or DVI(PC)>DP(monitor) adapter with certain restrictions:

1. Video adapters typically work only in one direction so be sure it's DVI(PC)>__(monitor),  or it specifically says "bidirectional".
2. Make sure the adapter supports the monitor's "recommended" resolution.
3. There are multiple types of DVI port, so the adapter has to support the DVI type on the video card.

From what I see, the NVDIA Quadro NVS 310 has 2 DP ports, not 2 HDMI ports, as you indicated. It only needs a 200 W PSU so it should work for you.

That page also lists other cards by their performance compared to the NVS 310. So compare their specs, including DirectX version support (higher=better), PSU requirements, ports, price, etc. To see if there's a better option. Not using video port adapters is always better...

@RoHe​ From the link you sent, It looks like NVS 310 has 2 Display Port, not DVI.
This is the link from NVDIA: https://images.nvidia.com/aem-dam/en-zz/Solutions/design-visualization/quadro-product-literature/NV-DS-NVS-310-May12-US-NV.pdf

It also has less performance compared to my current graphic card Intel HD 4600.
https://gpu.userbenchmark.com/Compare/Nvidia-NVS-310-vs-Intel-HD-4600-Desktop-125-GHz/m10691vs2168

Do you know any other graphic card that has 2 HDMI/DisplayPort and has comparable performance with my Intel HD 4600 and compatible with Inspron 3847?
Do you think NVIDIA GeForce GT 625 is better than NVIDIA NVS 310 although I need to use the DVI to HDMI/Display Port connector?

Thank you for your help.

No personal experience/recommendations for a video card for your Inspiron.

Let's back up...Which CPU do you have, Celeron, Pentium or Core i_ ?

Your userbenchmark link shows an NVS 310 add-in video card that's doesn't have a PCI-e x16 connector like the one here.

The Inspiron 3847 specs say Intel HD Graphics 4400/4600 is "integrated", but your link shows an add-in HD 4600 video card, which also doesn't appear to have an x16 connector. So those comparisons may not be relevant.

The link I posted above compares an NVS 310 card with PCI-e x16 connector to other add-in PCI-e x16 cards. So those are the comparisons I'd use. 

Any video card that needs a PSU 300W (or less), supports PCI-e 2.0, and has the right combination of ports for your needs should work. (A PCI-e 3.0 card should be backward compatible to PCI-e 2.0). A card that also has the highest amount of its own RAM, plus good graphics specs should be better.

As I also said above, you have to make sure any DVI port adapter is compatible with the type of DVI port on whichever card you choose. So if you decide on a card with DVI, only then look for a compatible adapter.  And, IMO, it's always better not to use adapters, if at all possible.

Up to you to decide which card and port combo works for your needs.

Few more things to consider...

You never mentioned what version of Windows you're running, so make sure whichever card you choose has a driver for that version. (Inspiron 3847 can run Win 7, Win 8.1, Win 10).

From what I've seen, many cards that should be compatible (eg, only need 300 W PSU) are somewhat older. So you might not be able to buy new. Don't know if you'd be willing to consider a used card...

@RoHe​   Here's my specs:
- Processor Intel(R) Core(TM) i7-4790 CPU @ 3.60GHz, 3601 Mhz, 4 Core(s), 8 Logical Processor(s)
- OS Name Microsoft Windows 10 Pro
- Installed Physical Memory (RAM) 16.0 GB
- BIOS Version/Date Dell Inc. A11, 5/7/2019
- SMBIOS Version 2.7
- BIOS Mode Legacy

I am wiling to buy used card (cheap). Is it going to be a problem with a used card?
Here's the diagram what I am trying to do. I'd like to have 2 different HDMI switch on purpose for flexibility. With my current BIOS, Can I use intel HD Graphics 4600 as the first HDMI and GeForce GT 705 as a second HDMI?  If yes, will it be automatically or I should do something? Or Is it better if I use DVI to HDMI cable?
Thank you for your help

Unless Inspiron 3847 BIOS has a Multi-Display option, I don't think you'll be able to use any of the onboard Intel Graphics ports when an add-in video card is installed.

Have no idea what you're proposing is going to work. Why do you need two HDMI switches?  Won't one KVM switch allow you to switch between PCs?

I know you were going to ask this. The setup is currently working for U2415 and 2412M using 1 HDMI switch and one VGA switch. I am planning on replacing 2412M with U2415 to avoid using VGA switch. One laptop for work, PC for personal.   If I use only one HDMI switch, I only can switch two monitor at a time (cannot split). With the second HDMI/VGA switch I can use the second monitor as an expansion monitor for work laptop or as personal use or vice versa (using first monitor as an expansion). You probably are going to ask me why not using remote desktop/VNC or synergy/mouse without borders. The reason is work laptop is completely locked down.  So, my thought is just use NVDIA GeForce GT705 and use DVI to HDMI cable, or use DisplayPort switch.   What do you think?  Thanks

Don't think you'll be able to use the onboard Intel HDMI port on the Inspiron when an add-in video card is installed.

If you can't find a compatible add-in card with 2 HDMI ports find a card with one HDMI and one DP, so you'd only need one DP(PC)>HDMI(monitor) adapter, if your switches don't support DP. The NVS 310 has two DP ports so you'd need to DP>HDMI adapters...

@RoHe​ It looks like your initial recommendation NVIDIA GeForce GT 705 is better than NVS 310.   Does DVI to HDMI cable work?   Thanks

DVI(PC)>HDMI(monitor) should would as long the adapter supports the type of DVI port that's on the card, and it's DVI(PC)>HDMI(monitor), not HDMI(PC)>DVI(monitor)...

Hello,
I checked on the BIOS setting and verified that Intel Multi-Display was enabled.
Does it mean I can use intel HD Graphics 4600 as the first HDMI and GeForce GT 705 as a second HDMI?

Thanks

With Multi-Display enabled on the Inspiron, and as long as at least one monitor is always connected to the add-in video card, you should be able to use the Intel Graphics HDMI port at same time.

If you switch the monitor that's connected to the add-in card HDMI to the other PC, you're likely going to get an error message on the Inspiron and its onboard HDMI port may stop working. 

On the other hand, if you switch the monitor that's connected to the onboard Intel Graphics HDMI port to the other PC, you should still be able to use the Inspiron at same time with just the monitor connected to the Inspiron's add-in video card.

You can tell Windows which monitor to use as primary on the Inspiron, and it can be either the one connected to the Intel HDMI port or to the add-in graphics card. But, better to set the one connected to the add-in card as primary, so you can switch the one connected to the onboard HDMI port to the other PC.

Bottom line, to use the Inspiron, always have a monitor connected to the add-in HDMI port, with or without a monitor connected to the onboard HDMI port.