I plan on upgrading my gfx card from a gtx 260 to a radeon 7870 or a gtx 570. i was just wondering if there would be any compatibility problems with my motherboard, it is a nforce 780i. a little bit old
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Nope. It'l work fine with a single card.
I think you should not have any slot bottleneck and any problem (PCI-E 2.0 to a PCI-E 3.0, you know).