#### Answer

$x=4$

#### Work Step by Step

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