Answer
$x=2-4 i, x=2+4 i$
Work Step by Step
Given \begin{equation}
-x^2+4 x=20.
\end{equation} Rearrange the equation so that there is a zero on the right hand side.
\begin{equation}
\begin{aligned}
-x^2+4 x&= 20\\
x^2-4 x&=-20\quad \text{Multiply by -1}\\
x^2-4 x+20&= 0.
\end{aligned}
\end{equation} Use the quadratic formula \begin{equation}
\begin{aligned}
x & =\frac{-(-4) \pm \sqrt{(-4)^2-4 \cdot 1\cdot (20)}}{2 \cdot 1}\\
& =\frac{4 \pm \sqrt{-64}}{2} \\
&= \frac{4 \pm 8i}{2} \\
\therefore x&= 2+4i\\
x&= 2-4i.
\end{aligned}
\end{equation} The solution is $x=2-4 i, x=2+4 i$.
