Would this card :
work on a pci express 4X 2.0 slot where it is actually a 3.0 16x card with the difference's in voltages?
The few benchmarks I could find show the stock 250 basically matching the stock 5750, so I would not consider the 250 to be an "upgrade" regarding performance versus your current 5750, unless you need DX12 or other features of the 250.
It should be backward compatible, so yes.
I don't want to buy a card that isn't backward compatible.
And what about the BUS speed and memory on a 4X 2.0 Slot is it compatible with 3.0 16X card mentioned above?
The other problem that might occur from using a 2.0 4x slot would be a bandwidth bottleneck that could give reduced performance versus a 2.0 8x or higher speed slot.
But it would be faster than the HD 5750 on that 2.0 4X slot?
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