Ok, I feel much better knowing that I should be ok power wise, but heres the final issue. Some people are saying it wont fit inside Dell OptiPlex desktops. Now, I don't have the desk top version, I have the tower version, but some people are even saying it wont fit in some bigger dell towers.
I know the situation, seen this many times, here is your PC below
The space between back panel and CPU cooler is 7.5 inches, which is applicable for cards with big cooler, if the card is skinny, as shown on the picture, it could be much longer.
Now about power requirements. 7750 can work on your 300 watt power supply, despite phony 400 watt manufacturer requirement, if in doubt - Dell offers 7750 as upgrade to your PC here http://accessories.dell.com/sna/productdetail.aspx?c=us&l=en&s=dhs&cs=19&sku=A6523076&mfgpid=192262
go to compatibility list, you will see 960 listed there.
So, please provide your GPU model, so I can look at newegg or Amazon for pictures, will take me 1 minutes to verify fit!