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 $ax^{2}+bx+c=0$.
$$2x^{2}-3x-8=0$$
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 $x=\frac{3±\sqrt{73}}{4}$ when $±$ is plus. Add $3$ to $\sqrt{73}$.
$$x=\frac{\sqrt{73}+3}{4}$$
Now solve the equation $x=\frac{3±\sqrt{73}}{4}$ when $±$ is minus. Subtract $\sqrt{73}$ from $3$.
$$x=\frac{3-\sqrt{73}}{4}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{3+\sqrt{73}}{4}$ for $x_{1}$ and $\frac{3-\sqrt{73}}{4}$ for $x_{2}$.
