Answer
$\frac{7 -\sqrt{949}}{18}\approx -1.32$, $\frac{7 + \sqrt{949}}{18}\approx 2.10$
Work Step by Step
Given \begin{equation}
-4.5 x^2+3.5 x+12.5=0.
\end{equation} Rearrange the equation before applying the quadratic formula and determine the constants $a$, $b$, $c$: \begin{equation}
\begin{aligned}
\left(-4.5 x^2+3.5 x+12.5\right)\cdot (-10)&=0\cdot (-10)\\
45x^2-35x-125&=0\\
ax^2+bx+c&=0\\
a =45\quad , b= -35\ , \quad c&= -125.
\end{aligned}
\end{equation} The quadratic formula gives: \begin{equation}
\begin{aligned}
x&=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\
x &=\frac{-(-35) \pm \sqrt{(-35)^2-4 \cdot 45(-125)}}{2 \cdot 45}\\
&=\frac{35 \pm \sqrt{23725}}{90}\\
&=\frac{35 \pm \sqrt{25\cdot 949}}{90}\\
&=\frac{35 \pm 5\sqrt{949}}{90}\\
&=5\cdot \frac{7\pm \sqrt{949}}{5\cdot 18}\\
&=\frac{7 \pm \sqrt{949}}{18}..
\end{aligned}
\end{equation} The solution is: \begin{equation}
x=\frac{7 -\sqrt{949}}{18}\approx -1.32,\quad x=\frac{7 + \sqrt{949}}{18}\approx 2.10.
\end{equation}
