Answer
The equation has no solutions.
Work Step by Step
$(3+\sqrt{x})^{2}+3(3+\sqrt{x})-10=0\qquad$...substitute $3+\sqrt{x}$ for $u$
$ u^{2}+3u-10=0\qquad$... solve with the Quadratic formula.
$u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$u=\displaystyle \frac{-3\pm\sqrt{9+40}}{2}$
$u=\displaystyle \frac{-3\pm\sqrt{49}}{2}$
$u=\displaystyle \frac{-3\pm 7}{2}$
$u=\displaystyle \frac{-3+7}{2}=\frac{4}{2}=2$ or $u=\displaystyle \frac{-3-7}{2}=\frac{-10}{2}=-5$
Bring back $3+\sqrt{x}=u$.
$3+\sqrt{x}=2$ or $3+\sqrt{x}=-5$
$\sqrt{x}=-1$ or $\sqrt{x}=-8$
$\sqrt{x}$ has to be a positive number which is why we discard both solutions.
The equation has no solutions.
