You can install most GPUs in Dell Optiplex 9xx MT or similar chassis. Even dual-slot, full length GPUs are no problem and I've seen people putting GTX970s in that chassis.
Unfortunately; your particular system has other problems:
1. The PCIe slot in the 790 models is undervolted so it can only supply 35W of power. Standard PCIe slots provide more than twice as much power (75W).
2. Your PSU is also VERY weak at just 265W and even if your slot was fully powered; the PSU wouldn't have been able to provide the necessary power to the GPU (75W).
There's a work around, though.
Get a dual-slot full length 950 with a 6-Pin power connector (Asus Strix x2, Gigabyte Windforce x2 come to mind), replace the PSU with a 400W one (Minimum) that has a 6-Pin PCIe power cable. There's a good chance that your GPU 'might' draw the rest of the power from the 6-Pin; instead of the PCIe slot and hence won't starve.
Will it work? I'm not entirely sure, as I personally haven't done it before but theoretically it should. It might burn your GPU or your Mobo or both but that's a worst case scenario.
Or just get a GT1030 (Preferably the GDDR5 variant) that has a TDP of just 30W. The GDDR4 variant has an even lower TDP of just 20W but... It's also 50% less powerful and hence is NOT recommended. Carefully read the specs as Nvidia is very discreet about it.
I hope it helps!