Let's hear the exact make and model PSU. I might give it a "barely passes" but the 750 is known for it's light load. Let's get the 960 model up in the discussion too.
Nice step up. Compare them at GPUBOSS to see how big a step.
I bought this starter rig a year or so ago and I've gotten great performance out of it, but it is showing it's age in the graphics department, I am NOT a techie, I dont have much experience with hardware or upgrading
Here is what I do know
It has an i7 4790S
16gb RAM
some kind of GYGABYTE motherboard
gtx 750 2gb
350w power supply

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