Answer
$\left\{ \dfrac{5-\sqrt{77}}{2},\dfrac{5+\sqrt{77}}{2} \right\}$
Work Step by Step
The standard form of the given equation, $
x^2-13=5x
,$ is
\begin{array}{l}\require{cancel}
x^2-5x-13=0
.\end{array}
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the quadratic equation, $
x^2-5x-13=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(-13)}}{2(1)}
\\\\=
\dfrac{5\pm\sqrt{25+52}}{2}
\\\\=
\dfrac{5\pm\sqrt{77}}{2}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{5-\sqrt{77}}{2},\dfrac{5+\sqrt{77}}{2} \right\}
.$
