A Sum of Roots

Algebra Level 2

The product of all real solutions to the equation 4x2+26x129812x4x220x+1734+2x81=0 \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 ab\frac{a}{b} where aa and bb are positive coprime integers. Find a+ba+b.

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