The case size will severely limit what you can install - rather than upgrade this "appliance", consider buying a full-size tower system to replace your current one -- this one will not be capable of much if any upgrading.
Well according to the spec sheet, it was validated with an GTX 750 Ti and lower, or an R9 360. Granted those are OEM cards so they were customized for the PSU output. You MIGHT be able to shove a 1050 or 1050 Ti inside as long as it does not require an external power connection, and have no issues. But in all honesty the computer wasn't really designed for it. And no it won't void the warranty if you upgrade it, unless you break the motherboard slot or some other component while installing a video card.
Yes, you could install one of the ITX 1050ti cards but I would recommend to not do it as Nvidia will release new less expensive graphics cards in 3 months. I'd say you should wait for the upcoming 20 series cards.
I do not work for dell. I am also a user.
what is the power supply of dell inspiron 3668? because the only thing i worry about is the power supply, i dont think that it can support gtx 1050ti which recommends 300w.
GIGABYTE GV-N1030D5-2GL GTX 1030 would not have issues.
1050ti is over priced due to currency mining and GDDR5 going thru the roof price wise.
I have added Asus 4gb GTX 1050Ti Graphics card
SanDisk 480gb SSD drive
Also added me spare 300gb 3.5" hard drive
Pc is now super fast with great graphics
all working with the original PSU 240w