#### Answer

$x=-3$

#### Work Step by Step

Isolate the square root on one side. Then square both sides and put all terms on one side. Factor by trial and error to solve for $x$. One of the answers does not work.
$\sqrt {2x+15}-6=x$
$(\sqrt {2x+15})^2=(x+6)^2$
$2x+15=x^2+12x+36$
$x^2+10x+21=0$
$(x+7)(x+3)=0$
$x=-7,-3$
$\sqrt {2\times-7+15}-6\ne-7$
$x=-3$