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 $ax^{2}+bx+c=0$.
$$6x^{2}+8x-1=0$$
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 $x=\frac{-8±2\sqrt{22}}{12}$ when $±$ is plus. Add $-8$ to $2\sqrt{22}$.
$$x=\frac{2\sqrt{22}-8}{12}$$
Divide $-8+2\sqrt{22}$ by $12$.
$$x=\frac{\sqrt{22}}{6}-\frac{2}{3}$$
Now solve the equation $x=\frac{-8±2\sqrt{22}}{12}$ when $±$ is minus. Subtract $2\sqrt{22}$ from $-8$.
$$x=\frac{-2\sqrt{22}-8}{12}$$
Divide $-8-2\sqrt{22}$ by $12$.
$$x=-\frac{\sqrt{22}}{6}-\frac{2}{3}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-\frac{2}{3}+\frac{\sqrt{22}}{6}$ for $x_{1}$ and $-\frac{2}{3}-\frac{\sqrt{22}}{6}$ for $x_{2}$.
