If this is your PSU, it has a 46A +12V rail and should be fine.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139028
That Corsair line isn't known for having the best capacitors, but it will handle the HD 7870. It is listed as having 2 PCIe connectors, so that won't be a problem.
If you doubt the room necessary for the gfx card, measure from the expansion slot on the back of the PC and check that against the length of the card. But since you already purchased the card, you'll know soon enough.