$x=\frac{\sqrt{11}\left(\sqrt{L}+1\right)}{11}$
$x=-\frac{\sqrt{11}\left(\sqrt{L}-1\right)}{11}$

$L=11x^{2}-2\sqrt{11}x+1$

$x=-\frac{\sqrt{11}\left(\sqrt{L}-1\right)}{11}$
$x=\frac{\sqrt{11}\left(\sqrt{L}+1\right)}{11}\text{, }L\geq 0$