Her desktop:

Dell OptiPlex 780 Mini Tower
Windows 7 Pro x64
4gb ram (so i probably have the A15 bios update).

I was wondering if this card will run on my Mother's desktop:

GT 730
Core Clock: 902 MHz

Video Memory: 2GB DDR3

Memory Interface: 64-bit

Bus: PCI Express 2.0 x16 (x8 lanes)

She has plenty of space for a large card to plug in, so size does not matter.