Answer
$x = -2.48, x= 2.15$
Work Step by Step
Use either the square root method, the quadratic formula or factoring.
$$
\begin{aligned}
\frac{3}{4} x^2+\frac{1}{2} x-7 & =\frac{1}{4} x-3 \\
\frac{3}{4} x^2+\frac{1}{2} x & =\frac{1}{4} x-3+7 \\
\left(\frac{3}{4} x^2+\frac{1}{2} x\right) \cdot 4 & =\left(\frac{1}{4} x+4\right) \cdot 4 \\
3 x^2+2 x & =x+16 \\
3 x^2+2 x-x & =16 \\
3 x^2+x & =16.
\end{aligned}
$$ Bring the equation to the standard form and solve it.
$$
\begin{aligned}
& 3 x^2+x-16=0 \\
& \begin{aligned}
x & =\frac{-1 \pm \sqrt{1^2+4(16)(3)}}{2(3)} \\
& =\frac{-1 \pm \sqrt{193}}{6} \\
& \approx0.1667 \pm 2.315.
\end{aligned}
\end{aligned}
$$ We have: $$
\begin{aligned}
x & =-0.1667-2.315 \\
& =-2.48
\end{aligned}$$ $$\begin{aligned}
x & =-0.1167+2.315 \\
& =2.15
\end{aligned}$$ Define the following version of the function and plot it. We see that the zeros are where they should be.
$$
f(x)= \frac{3}{4} x^2+\frac{1}{4} x-4.$$
