motherboard has 2.0 pci express x16 BUT graphics card has 3.0 x16 pci express

serge44

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PCIe 3.0 cards are backward compatible with PCIe 2.0, so it'll work. Besides that, PCIe has very wide bandwith, and most current cards can't even fill 2.0 bandwith.

So yeah, you'll be fine. At least regarding PCIe compatibility.
 

serge44

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Backward compatibility means that certain technology is compatible with previous generations of the same technology. For example, USB 3.0 ports will work with USB 1.0 and 2.0 devices when you plug them in, because they're backward compatible.
 

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