I dont really think is enough! 24A at 12v is pretty decent! Try it , dont worrie even if is not enough power the PC parts wont be damaged.If the PC will shut down or wont power up or low performance on full load is beacause the PSU is too weak.
If your PSU doesn't have a PCIE power connector, chances are it doesn't really have enough amperage available on +12V to run a powerful video card, regardless of what the label says. I would NOT use adapters, as contrary to GoldenGPU's post, a cheap PSU can die violently, sometimes taking attached parts with it into the fiery abyss.
A quality modern PSU has full range active PFC (no little voltage switch), and some level of 80+ certification. Seasonic, Antec, Corsair, XFX, and Enermax/LEPA are among the better brands.