$x=\frac{\sqrt{8A+1}-3}{4}$
$x=\frac{-\sqrt{8A+1}-3}{4}$

$A=\left(x+1\right)\left(2x+1\right)$

$x=\frac{\sqrt{8A+1}-3}{4}$
$x=\frac{-\sqrt{8A+1}-3}{4}\text{, }A\geq -\frac{1}{8}$