Answer
$x=3$
Work Step by Step
The value of $x$ that satisfies the equation $
\sqrt{3x+6}-\sqrt{7x-6}=0
$ is
\begin{array}{l}\require{cancel}
\sqrt{3x+6}=\sqrt{7x-6}
\\
\left( \sqrt{3x+6} \right)^2=\left( \sqrt{7x-6} \right)^2
\\
3x+6=7x-6
\\
3x-7x=-6-6
\\
-4x=-12
\\
x=3
.\end{array}
