$\alpha =-x\left(5x-11\right)$

$x=\frac{\sqrt{121-20\alpha }+11}{10}$
$x=\frac{-\sqrt{121-20\alpha }+11}{10}$

$x=\frac{\sqrt{121-20\alpha }+11}{10}$
$x=\frac{-\sqrt{121-20\alpha }+11}{10}\text{, }\alpha \leq \frac{121}{20}$