Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$20x^{2}-80x-36=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
Now solve the equation $x=\frac{80±8\sqrt{145}}{40}$ when $±$ is plus. Add $80$ to $8\sqrt{145}$.
$$x=\frac{8\sqrt{145}+80}{40}$$
Divide $80+8\sqrt{145}$ by $40$.
$$x=\frac{\sqrt{145}}{5}+2$$
Now solve the equation $x=\frac{80±8\sqrt{145}}{40}$ when $±$ is minus. Subtract $8\sqrt{145}$ from $80$.
$$x=\frac{80-8\sqrt{145}}{40}$$
Divide $80-8\sqrt{145}$ by $40$.
$$x=-\frac{\sqrt{145}}{5}+2$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $2+\frac{\sqrt{145}}{5}$ for $x_{1}$ and $2-\frac{\sqrt{145}}{5}$ for $x_{2}$.
