Answer
$x=1.5-0.5\sqrt{105}, x=1.5+0.5\sqrt{105}$
Work Step by Step
Use the completing the square method. $$
\begin{aligned}
\frac{1}{4} x^2-\frac{3}{4} x+7 & =13 \\
\frac{x^2}{4}-\frac{3 x}{4} & =13-7 \\
\left(\frac{x^2}{4}-\frac{3 x}{4}\right) \cdot 4 & =6(4)\\
x^2-3 x+1.5^2 & =24+1.5^2 \\
(x-1.5)^2 & =26.25 \\
x-1.5 & = \pm \sqrt{26.25} \\
x & = 1.5 \pm 0.5\sqrt{105}.
\end{aligned}
$$ This gives the solution: $$
\begin{aligned}
x & =1.5-0.5\sqrt{105} \\
& \approx -3.62347 \\
x & =1.5+0.5\sqrt{105} \\
& \approx 6.62347.
\end{aligned}
$$ Define the following version of the function and plot it. We see that the zeros are where they should be. $$
f(x) =(x-1.5)^2-26.25.
$$
