Answer
$x=-8$ and $x=-6$
Work Step by Step
Add $12$ to both sides:
$$\frac{1}{4}x^2+\frac{7}{2}x+12=0$$
Multiply $4$ to both sides:
\begin{align*}
4\left(\frac{1}{4}x^2+\frac{7}{2}x+12\right)&=4(0)\\\\
4\left(\frac{1}{4}\right)x^2+4\left(\frac{7}{2}x\right)+4(12)&=0\\\\
x^2+14x+48=0
\end{align*}
Factor the trinomial:
\begin{align*}
(x+8)(x+6)&=0
\end{align*}
Use the Zero-Product Property by equating each factor to zero, then solve each equation:
\begin{align*}
x+8&=0 &\text{or}*& &x+6=0\\
x&=-8 &\text{or}& &x=-6
\end{align*}
