Yes, it will. x16 is the main type of PCI-E for GPUs, and 3.0 is just a generation, and is backwards compatible as well.
Just to be sure, what's your motherboard?
@Shektron,I ran Speccy its showing as Lenovo LGA-775 Motherboard.
Actually it's Lenovo ThinkCenter M57_6075 motherboard.https://support.lenovo.com/us/en/solutions/migr-68844
According to it's Site it's giving following Info about Expansion Slots :
1.Slot 1: Full height, PCI Express x16 2.Slot 2: Full height, PCI Express x1 3.Slot 3: Full height, half length PCI 4.Slot 4: Full height, half length PCI
Specs page doesn't actually specify which generation the slots conform to (eg PCEe 1.0, 2.0, or 3.0) but a 3.0 card will definitly fit and work - - - you won't notice any discernible performance issues if it's a PCIe 2.0 slot, but you probably will if it's only the original PCIe 1.0
It'll work just fine. But the GT 730 really isn't for gaming, so if you want to use the graphics card for gaming(which is the typical use for it) then you should really consider increasing your budget to at least a GTX 750 Ti. If you can't afford a new one, try buying used from a trusted source. It'll really help a lot on performance. The GT 730, excuse the language, won't run sh*t.