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Let the unknown integer by n.

2n = 6 + 2n2 : 2n2 - 2n + 6 = 0

For a quadratic equation an2 + bn + c = 0 then the equation has no real roots if

b2 - 4ac < 0 : In the example b2 - 4ac = 4 -48 = -44 as this < 0 then the original expression cannot have a real integer solution.

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