Answer
x=-2
Work Step by Step
Multiply $\frac{3}{4}$ to both sides:
$\frac{3}{4} \cdot \frac{4}{3}\arctan{(\frac{x}{2})}=\pi \cdot \frac{3}{4}
\\\arctan{(\frac{x}{2})}=\frac{3\pi}{4}$
RECALL:
$\arctan{(x)} = \theta \longrightarrow \tan{\theta} = x$
Use the rule above to obtain:
$\arctan{(\frac{x}{2})} = \frac{3\pi}{4}
\\\tan{(\frac{3\pi}{4})}=\frac{x}{2}
\\-1=\frac{x}{2}
\\-1(2)=x
\\-2=x$
