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 $ax^{2}+bx+c=0$.
$$4x^{2}-18x-6=0$$
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 $x=\frac{18±2\sqrt{105}}{8}$ when $±$ is plus. Add $18$ to $2\sqrt{105}$.
$$x=\frac{2\sqrt{105}+18}{8}$$
Divide $18+2\sqrt{105}$ by $8$.
$$x=\frac{\sqrt{105}+9}{4}$$
Now solve the equation $x=\frac{18±2\sqrt{105}}{8}$ when $±$ is minus. Subtract $2\sqrt{105}$ from $18$.
$$x=\frac{18-2\sqrt{105}}{8}$$
Divide $18-2\sqrt{105}$ by $8$.
$$x=\frac{9-\sqrt{105}}{4}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{9+\sqrt{105}}{4}$ for $x_{1}$ and $\frac{9-\sqrt{105}}{4}$ for $x_{2}$.
