I don't know that Dell system.
But if it has a free PCI-E slot (which it should have when removing your current card) and can deliver the
case cooling and also
power needs of the new card, it should work.
Maybe some hardware expert from your friends can help you there, checking this highlighted stuff before buying.
The more powerful cards produce a lot of heat and need much more power than your current card, so a closer look is recommended. If Dell e. g. used a small power supply, you won't get a stable system there.
Otherwise, a shop has to help, but will need money for this.
I think that AMD recommends a 500W PSU for that card and I don't know if Dell included such a thing. The case cooling also needs some 'flow' to allow a safe operation which also covers the noise produced.
They usually recommend too high PSU values there, to be on the safe side. But let those decisions be up to a guy with some hardware knowledge, when looking at your system more closely.
But maybe try those replacement clouds (and slider settings) I spoke of. They are cheap or come at no costs and might help a bit, before buying new hardware.