RE: Dell Inspiron 3847 PSU upgrade
There are certainly upgraded PSUs you can run in a 3847. The connector is standard, but your older power supply may not supply enough of the right kind of power.
If you bought a newer PSU with the right specs I'm 99% it will work and I'm also fairly sure the 24 pin ATX connector is standard. It has been for a while.
What do you need more power for? How much more?
I don't have any specific recommendations because I don't know the size of your case and how large of a PSU will fit that case and how much power you need.