Let (α, β) be the centroid of the triangle formed by the lines 15 x-y=82,6 x-5 y=-4 and 9 x+4 y=17. Then α+2 β and 2 α-β are the roots of the equation

Let $\displaystyle (\alpha, \beta)$ be the centroid of the triangle formed by the lines $\displaystyle 15 x-y=82,6 x-5 y=-4$ and $\displaystyle 9 x+4 y=17$. Then $\displaystyle \alpha+2 \beta$ and $\displaystyle 2 \alpha-\beta$ are the roots of the equation