A Fermat's Problem

How many pairs \((x, y)\) of non-negative integers with \(0\le x\le y\) satisfy the equation \(5{ x }^{ 2 }-4xy+2x+{ y }^{ 2 }=624\)?


This problem has been taken from 2015 Fermat Contest. (Please don't suppose that Fermat created it)
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