$$x^{2}+6x-\sqrt{x^{2}+6x}=\sqrt{2}$$
$x=-\frac{\sqrt{2\sqrt{4\sqrt{2}+1}+4\sqrt{2}+38}}{2}-3\approx -6.493459257$
$x=\frac{\sqrt{2\sqrt{4\sqrt{2}+1}+4\sqrt{2}+38}}{2}-3\approx 0.493459257$
