$I=-x\left(3x-5\right)$

$x=\frac{\sqrt{25-12I}+5}{6}$
$x=\frac{-\sqrt{25-12I}+5}{6}$

$x=\frac{\sqrt{25-12I}+5}{6}$
$x=\frac{-\sqrt{25-12I}+5}{6}\text{, }I\leq \frac{25}{12}$