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