There is an easy way to tell yourself if the PSU you intend to buy will work fine.
First find out the requirements of power the new graphics card needs to run right from the PSU.
Radeon 6870 graphics card.
Power Consumption (load) 245W max
Amps required by the 12v power rail of the PSU for the card to run =13.5 Amps
Now you need to check what the PSU can output on its 12v power rails. Looks ok to me