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 $ax^{2}+bx+c=0$.
$$13x^{2}-4x-18=0$$
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 $x=\frac{4±2\sqrt{238}}{26}$ when $±$ is plus. Add $4$ to $2\sqrt{238}$.
$$x=\frac{2\sqrt{238}+4}{26}$$
Divide $4+2\sqrt{238}$ by $26$.
$$x=\frac{\sqrt{238}+2}{13}$$
Now solve the equation $x=\frac{4±2\sqrt{238}}{26}$ when $±$ is minus. Subtract $2\sqrt{238}$ from $4$.
$$x=\frac{4-2\sqrt{238}}{26}$$
Divide $4-2\sqrt{238}$ by $26$.
$$x=\frac{2-\sqrt{238}}{13}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{2+\sqrt{238}}{13}$ for $x_{1}$ and $\frac{2-\sqrt{238}}{13}$ for $x_{2}$.
