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 $ax^{2}+bx+c=0$.
$$15a^{2}+3a-4=0$$
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 $a=\frac{-3±\sqrt{249}}{30}$ when $±$ is plus. Add $-3$ to $\sqrt{249}$.
$$a=\frac{\sqrt{249}-3}{30}$$
Divide $-3+\sqrt{249}$ by $30$.
$$a=\frac{\sqrt{249}}{30}-\frac{1}{10}$$
Now solve the equation $a=\frac{-3±\sqrt{249}}{30}$ when $±$ is minus. Subtract $\sqrt{249}$ from $-3$.
$$a=\frac{-\sqrt{249}-3}{30}$$
Divide $-3-\sqrt{249}$ by $30$.
$$a=-\frac{\sqrt{249}}{30}-\frac{1}{10}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-\frac{1}{10}+\frac{\sqrt{249}}{30}$ for $x_{1}$ and $-\frac{1}{10}-\frac{\sqrt{249}}{30}$ for $x_{2}$.
