A Sum of Roots

Algebra Level 2

The product of all real solutions to the equation \[ \begin{array} {l l} \sqrt{4x^2+26x-129} - \sqrt{81 - 2x} \\ - \sqrt{4x^2 - 20x + 1734} + \sqrt{2x - 81} = 0 \\ \end{array} \] can be written as \(\frac{a}{b} \) where \(a\) and \(b\) are positive coprime integers. Find \(a+b\).

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