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 $ax^{2}+bx+c=0$.
$$5x^{2}-14x-2=0$$
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 $x=\frac{14±2\sqrt{59}}{10}$ when $±$ is plus. Add $14$ to $2\sqrt{59}$.
$$x=\frac{2\sqrt{59}+14}{10}$$
Divide $14+2\sqrt{59}$ by $10$.
$$x=\frac{\sqrt{59}+7}{5}$$
Now solve the equation $x=\frac{14±2\sqrt{59}}{10}$ when $±$ is minus. Subtract $2\sqrt{59}$ from $14$.
$$x=\frac{14-2\sqrt{59}}{10}$$
Divide $14-2\sqrt{59}$ by $10$.
$$x=\frac{7-\sqrt{59}}{5}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{7+\sqrt{59}}{5}$ for $x_{1}$ and $\frac{7-\sqrt{59}}{5}$ for $x_{2}$.
