That card should work with your system. There were optional discrete graphics cards for the 580s. The recommended PSU for the GT 730 is 300 watts minimum, so you"ll need to check yours. If you have a 230 watt PSU, you may need to swap that out, too.
I have 250 Watt PSU, but since it's Dell's factory model, I'll try to give it a go. What I'm actually worried about is physical space available, my motherboard seems to be too congested.