Answer
$2$
Work Step by Step
$\sqrt {x+4}=\sqrt{3x}$
Square both sides:
$(\sqrt {x+4})^2=(\sqrt{3x})^2$
$x+4=3x$
Subtract $x$ from both sides:
$x+4-x=3x-x$
$4=2x$
Divide both sides by $2$:
\begin{align*}
\frac42&=\frac{2x}2\\\\
2&=x\end{align*}
Substitute into original problem to check for extraneous solutions:
$\sqrt {(2)+4}=\sqrt{3(2)}$
$\sqrt {6}=\sqrt{6}$
$6=6$