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 $ax^{2}+bx+c=0$.
$$7y^{2}+8y-5=0$$
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 $y=\frac{-8±2\sqrt{51}}{14}$ when $±$ is plus. Add $-8$ to $2\sqrt{51}$.
$$y=\frac{2\sqrt{51}-8}{14}$$
Divide $-8+2\sqrt{51}$ by $14$.
$$y=\frac{\sqrt{51}-4}{7}$$
Now solve the equation $y=\frac{-8±2\sqrt{51}}{14}$ when $±$ is minus. Subtract $2\sqrt{51}$ from $-8$.
$$y=\frac{-2\sqrt{51}-8}{14}$$
Divide $-8-2\sqrt{51}$ by $14$.
$$y=\frac{-\sqrt{51}-4}{7}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{-4+\sqrt{51}}{7}$ for $x_{1}$ and $\frac{-4-\sqrt{51}}{7}$ for $x_{2}$.
