Answer
$x=\left\{
2-i\sqrt{6}, 2+i\sqrt{6}
\right\}
$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation,
\begin{align*}
-x^2+4x&=10
\\
-x^2+4x-10&=0
,\end{align*} has $a=
-1
,$ $b=
4
,$ and $c=
-10
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}
x&=\dfrac{-4\pm\sqrt{4^2-4(-1)(-10)}}{2(-1)}
\\\\&=
\dfrac{-4\pm\sqrt{16-40}}{-2}
\\\\&=
\dfrac{-4\pm\sqrt{-24}}{-2}
\\\\&=
\dfrac{-4\pm\sqrt{-1}\cdot\sqrt{4}\cdot\sqrt{6}}{-2}
\\\\&=
\dfrac{-4\pm\sqrt{-1}\cdot2\sqrt{6}}{-2}
\\\\&=
\dfrac{-4\pm i\cdot2\sqrt{6}}{-2}
&\text{ (use $i=\sqrt{-1}$)}
\\\\&=
\dfrac{-4\pm 2i\sqrt{6}}{-2}
\\\\&=
\dfrac{\cancel{-4}^2\pm \cancel{2}^{-1}i\sqrt{6}}{\cancel{-2}^1}
&\text{ (divide by $-2$)}
\\\\&=
2\pm i\sqrt{6}
.\end{align*}
The solutions are $
x=\left\{
2-i\sqrt{6}, 2+i\sqrt{6}
\right\}
.$