Answer
$x = -7.59 $ or $ x= 1.79$
Work Step by Step
Multiply both sides by $10$ then use the quadratic formula. $$
\begin{aligned}
9.9 x^2+57.4 x-134.8&=0\\
99 x^2+574 x-1348=0
\end{aligned}
$$ $$
\begin{aligned}
a & =99 \\
b& =574\\
d & =-1348 \\
\end{aligned}
$$ $$
\begin{aligned}
x&= \frac{-b\pm \sqrt{b^2-4ac}}{2a}\\
x& =\frac{-(574) \pm \sqrt{(574)^2-4 \cdot 99 \cdot (-1348)}}{2 \cdot 99 }\\
& =\frac{-574 \pm \sqrt{863284}}{198}.
\end{aligned}
$$ This gives $$
\begin{aligned}
x & =\frac{-574 - \sqrt{863284}}{198} \\
& \approx-7.59\\
x & =\frac{-574 + \sqrt{863284}}{198} \\
& \approx1.79
\end{aligned}
$$ We got: $$x = -7.59 \text{ or } x= 1.79.$$ Define the following function and plot it. We see that the zeros are where they should be. $$
f(x) =9.9 x^2+57.4 x-134.8
$$
