Answer
$x=3$
Work Step by Step
Raising both sides to the $\text{
2nd
}$ power, the solution to the given equation, $
\sqrt{5x+1}=4
$, is
\begin{array}{l}
5x+1=16
\\\\
5x=16-1
\\\\
5x=15
\\\\
x=\dfrac{15}{5}
\\\\
x=3
.\end{array}
Upon checking, $
x=3
$ satisfies the given equation.