Answer
$x= 9$
Work Step by Step
Given \begin{equation}
\sqrt{2 x+5}=\sqrt{3 x-4}.
\end{equation} Start by squaring both sides of the equation to eliminate the radical sign and solve for $x$. \begin{equation}
\begin{aligned}
\sqrt{2 x+5}&=\sqrt{3 x-4} \\
\left( \sqrt{2 x+5} \right)^2&= \left( \sqrt{3 x-4} \right)^2\\
2 x+5& = 3 x-4\\
5+4& = 3x-2x\\9& =x.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt{2 \cdot 9+5}& \stackrel{?}{=} \sqrt{3 \cdot 9-4} \\
\sqrt{23}& =\sqrt{23}\checkmark.
\end{aligned}
\end{equation} The solution is $x= 9$.
