#### Answer

$x=5$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt{3x+1}-4=0
,$ use the properties of equality to isolate the radical expression. The square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{3x+1}=4
.\end{array}
Squaring both sides of the equation results to
\begin{array}{l}\require{cancel}
\left( \sqrt{3x+1} \right)^2=(4)^2
\\\\
3x+1=16
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
3x=16-1
\\\\
3x=15
\\\\
x=\dfrac{15}{3}
\\\\
x=5
.\end{array}
Upon checking, $
x=5
$ satisfies the original equation.