Answer
$\frac{233}{2}$.
Work Step by Step
$\sqrt{2x-8}=15$
Squaring both sides of the equation,
$\begin{align}
& \sqrt{2x-8}=15 \\
& {{\left( \sqrt{2x-8} \right)}^{2}}={{\left( 15 \right)}^{2}} \\
& 2x-8=225
\end{align}$
Add $\left( 8 \right)$ to both sides.
$\begin{align}
& 2x-8=225 \\
& 2x-8+8=225+8 \\
& 2x=233
\end{align}$
Divide by $2$ on both sides,
$\begin{align}
& 2x=233 \\
& \frac{2x}{2}=\frac{233}{2} \\
& x=\frac{233}{2}
\end{align}$
Thus, the required value is $x=\frac{233}{2}$.
