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 $ax^{2}+bx+c=0$.
$$20x^{2}-28x-36=0$$
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 $x=\frac{28±4\sqrt{229}}{40}$ when $±$ is plus. Add $28$ to $4\sqrt{229}$.
$$x=\frac{4\sqrt{229}+28}{40}$$
Divide $28+4\sqrt{229}$ by $40$.
$$x=\frac{\sqrt{229}+7}{10}$$
Now solve the equation $x=\frac{28±4\sqrt{229}}{40}$ when $±$ is minus. Subtract $4\sqrt{229}$ from $28$.
$$x=\frac{28-4\sqrt{229}}{40}$$
Divide $28-4\sqrt{229}$ by $40$.
$$x=\frac{7-\sqrt{229}}{10}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{7+\sqrt{229}}{10}$ for $x_{1}$ and $\frac{7-\sqrt{229}}{10}$ for $x_{2}$.
