Answer
The equation has no solutions.
Work Step by Step
$(1+\sqrt{x})^{2}+5(1+\sqrt{x})+6=0\qquad$...substitute $1+\sqrt{x}$ for $u$
$ u^{2}+5u+6=0\qquad$... solve with the Quadratic formula.
$u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$u=\displaystyle \frac{-5\pm\sqrt{25-24}}{2}$
$u=\displaystyle \frac{-5\pm\sqrt{1}}{2}$
$u=\displaystyle \frac{-5\pm 1}{2}$
$u=\displaystyle \frac{-5+1}{2}=\frac{-4}{2}=-2$ or $u=\displaystyle \frac{-5-1}{2}=\frac{-6}{2}=-3$
Bring back $1+\sqrt{x}=u$.
$1+\sqrt{x}=-2$ or $1+\sqrt{x}=-3$
$\sqrt{x}=-3$ or $\sqrt{x}=-2$
$\sqrt{x}$ has to be a positive number which is why we discard both solutions.
The equation has no solutions.