Answer
$x= 4$
Work Step by Step
Given \begin{equation}
\sqrt{2+5 x}=\sqrt{3 x+10}.
\end{equation} Start by squaring both sides of the equation to eliminate the radical signs and solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt{2+5 x}&=\sqrt{3 x+10}\\
\left( \sqrt{2+5 x}\right)^2&= \left(\sqrt{3 x+10}\right)^2\\
2+5 x& = 3 x+10\\
5 x-3x& = 10-2\\
2x& =8\\
x&=4.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt{2+ 5\cdot (4)}& \stackrel{?}{=} \sqrt{3\cdot (4)+10} \\
\sqrt{22}& =\sqrt{22}\checkmark.
\end{aligned}
\end{equation} The solution is $x= 4$.
