Unoriginal

I've bought some new books for my 14th birthday. (Don't judge me!) One of them is a really great book about inequalities. Let's take one problem from it.

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$x$ and $y$ are two real number that satisfy $x \ne -2y$ and

$\dfrac{(2x^2 + 13y^2 - xy)^2 - 6xy + 9}{(x +2y)^2} = 6$

Calculate $x > 0$ .

If $x = a \sqrt{\dfrac{b}{c}}$ , where $a,b,c$ are positive integers, $b,c$ coprime and $c + a = 31$ , then enter $ca + b$ as your answer.

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This is part of the series: " It's easy, believe me! "