Answer
$g= 8.567$
Work Step by Step
Givdn \begin{equation}
2.4 \sqrt{2.5 g+4}-7.5=4.6.
\end{equation} Start by rearranging the equation and squaring both sides of the equation to eliminate the radical sign and solve for $g$. \begin{equation}
\begin{aligned}
2.4 \sqrt{2.5 g+4}-7.5&=4.6 \\
2.4 \sqrt{2.5 g+4}=12.1\\
\left( 2.4 \sqrt{2.5 g+4} \right)^2&= \left( 12.1 \right)^2\\
5.76\cdot (2.5 g+4)& = 146.41\\
14.4g+23.04& = 146.41\\
g& =\frac{146.41-23.04}{14.4}\\
&\approx 8.567361.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
2.4\sqrt{2.5 \cdot 8.567361+4}-7.5 & \stackrel{?}{=} 4.6 \\
4.6& \approx4.6\checkmark.
\end{aligned}
\end{equation}
The solution is $g= 8.567$
