Answer
$ x =\frac{9 - \sqrt{257}}{22}, x=\frac{9 + \sqrt{257}}{22}$
Work Step by Step
Use the quadratic formula. $$
\begin{aligned}
\frac{11}{21} x^2-\frac{9}{21} x-\frac{4}{21} & =0 \\
\frac{11 x^2-9 x-4}{21} \cdot(21) & =0 \cdot(21) \\
11 x^2-9 x-4 & =0.
\end{aligned}
$$ Set $$
\begin{aligned}
& a=11 \\
& b=-9 \\
& c=-4
\end{aligned}
$$ $$
\begin{aligned}
x & =\frac{-(-9) \pm \sqrt{(-9)^2-4 \cdot 11(-4)}}{2 \cdot 11} \\
& =\frac{9 \pm \sqrt{257}}{22}.
\end{aligned}
$$ This gives $$
\begin{aligned}
x & =\frac{9 - \sqrt{257}}{22}\\
& \approx -0.31960\\
x & =\frac{9 +\sqrt{257}}{22} \\
& \approx 1.13778.
\end{aligned}
$$ Define the following function and plot it. We see that the zeros are where they should be.
$$
f(x) = 11 x^2-9 x-4.
$$
