Answer
$x=4$
Work Step by Step
Raising both sides to the $\text{
2nd
}$ power, the solution to the given equation, $
\sqrt{7x-3}=5
$, is
\begin{array}{l}
7x-3=25
\\\\
7x=25+3
\\\\
7x=28
\\\\
x=\dfrac{28}{7}
\\\\
x=4
.\end{array}
Upon checking, $
x=4
$ satisfies the given equation.