Answer
$x=5$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt{9x-4}=\sqrt{8x+1}
,$ 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( \sqrt{9x-4} \right)^2=\left( \sqrt{8x+1} \right)^2
\\\\
9x-4=8x+1
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
9x-8x=1+4
\\\\
x=5
.\end{array}
Upon checking, $
x=5
$ satisfies the original equation.