Answer
$x\approx2.197$
Work Step by Step
Subtract $7$ from each side to obtain:
\begin{align*}
7-2e^{\frac{x}{2}}-7&=1-7\\\\
-2e^{\frac{x}{2}}&=-6\\\\
\frac{-2e^{\frac{x}{2}}}{-2}&=\frac{-6}{-2}\\\\
e^{\frac{x}{2}}&=3
\end{align*}
RECALL:
$$\ln{x}=y \longleftrightarrow e^y=x$$
Use the definition above to obtain:
\begin{align*}
\ln{3}&=\frac{x}{2}\\\\
2(\ln3)&=2\left(\frac{x}{2}\right)\\\\
2\ln3&=x
\end{align*}
Use a scientific calculator to obtain:
$$x\approx 2.197$$