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 $ax^{2}+bx+c=0$.
$$3x^{2}+x-1=0$$
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 $x=\frac{-1±\sqrt{13}}{6}$ when $±$ is plus. Add $-1$ to $\sqrt{13}$.
$$x=\frac{\sqrt{13}-1}{6}$$
Now solve the equation $x=\frac{-1±\sqrt{13}}{6}$ when $±$ is minus. Subtract $\sqrt{13}$ from $-1$.
$$x=\frac{-\sqrt{13}-1}{6}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{-1+\sqrt{13}}{6}$ for $x_{1}$ and $\frac{-1-\sqrt{13}}{6}$ for $x_{2}$.
