Answer
$x=\dfrac{39}{7}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt{7x-3}=6
,$ square both sides of the equation and then isolate the variable. Then, 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{7x-3} \right)^2=(6)^2
\\\\
7x-3=36
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
7x=36+3
\\\\
7x=39
\\\\
x=\dfrac{39}{7}
.\end{array}
Upon checking, $
x=\dfrac{39}{7}
$ satisfies the original equation.