#### Answer

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
x=\sqrt{x^2+3x+9}
,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation.
$\bf{\text{Solution Details:}}$
Squaring both sides of the equation results to
\begin{array}{l}\require{cancel}
\left( x \right)^2=\left( \sqrt{x^2+3x+9} \right)^2
\\\\
x^2=x^2+3x+9
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x^2-x^2-3x=9
\\\\
-3x=9
\\\\
x=\dfrac{9}{-3}
\\\\
x=-3
.\end{array}
Upon checking, $
x=-3
$ DOES NOT satisfy the original equation. Hence, there is $\text{
no solution
.}$