Answer
$x=2\pm\sqrt{6}$
Work Step by Step
Using the Distributive Property and the properties of equality, the given quadratic equation, $
x(x-2)=5
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2-2x=5
\\\\
x^2-2x-5=0
.\end{array}
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are
\begin{array}{l}\require{cancel}
x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(-5)}}{2(1)}
\\\\
x=\dfrac{4\pm\sqrt{4+20}}{2}
\\\\
x=\dfrac{4\pm\sqrt{24}}{2}
\\\\
x=\dfrac{4\pm\sqrt{4\cdot6}}{2}
\\\\
x=\dfrac{4\pm\sqrt{(2)^2\cdot6}}{2}
\\\\
x=\dfrac{4\pm2\sqrt{6}}{2}
\\\\
x=\dfrac{2(2\pm\sqrt{6})}{2}
\\\\
x=\dfrac{\cancel{2}(2\pm\sqrt{6})}{\cancel{2}}
\\\\
x=2\pm\sqrt{6}
.\end{array}
