#### Answer

$x=7$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt{4x-2}=\sqrt{3x+5}
,$ 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{4x-2} \right)^2=\left( \sqrt{3x+5} \right)^2
\\\\
4x-2=3x+5
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
4x-3x=5+2
\\\\
x=7
.\end{array}
Upon checking, $
x=7
$ satisfies the original equation.