#### Answer

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
x=\sqrt{x^2-4x-8}
,$ 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^2-4x-8} \right)^2
\\\\
x^2=x^2-4x-8
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x^2-x^2+4x=-8
\\\\
4x=-8
\\\\
x=-\dfrac{8}{4}
\\\\
x=-2
.\end{array}
Upon checking, $
x=-2
$ DOES NOT satisfy the original equation. Hence, there is $\text{
no solution
.}$