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 $ax^{2}+bx+c=0$.
$$9x^{2}-10x+2=0$$
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 $x=\frac{10±2\sqrt{7}}{18}$ when $±$ is plus. Add $10$ to $2\sqrt{7}$.
$$x=\frac{2\sqrt{7}+10}{18}$$
Divide $10+2\sqrt{7}$ by $18$.
$$x=\frac{\sqrt{7}+5}{9}$$
Now solve the equation $x=\frac{10±2\sqrt{7}}{18}$ when $±$ is minus. Subtract $2\sqrt{7}$ from $10$.
$$x=\frac{10-2\sqrt{7}}{18}$$
Divide $10-2\sqrt{7}$ by $18$.
$$x=\frac{5-\sqrt{7}}{9}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{5+\sqrt{7}}{9}$ for $x_{1}$ and $\frac{5-\sqrt{7}}{9}$ for $x_{2}$.
