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 $ax^{2}+bx+c=0$.
$$-4x^{2}+10x-3=0$$
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 $x=\frac{-10±2\sqrt{13}}{-8}$ when $±$ is plus. Add $-10$ to $2\sqrt{13}$.
$$x=\frac{2\sqrt{13}-10}{-8}$$
Divide $-10+2\sqrt{13}$ by $-8$.
$$x=\frac{5-\sqrt{13}}{4}$$
Now solve the equation $x=\frac{-10±2\sqrt{13}}{-8}$ when $±$ is minus. Subtract $2\sqrt{13}$ from $-10$.
$$x=\frac{-2\sqrt{13}-10}{-8}$$
Divide $-10-2\sqrt{13}$ by $-8$.
$$x=\frac{\sqrt{13}+5}{4}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{5-\sqrt{13}}{4}$ for $x_{1}$ and $\frac{5+\sqrt{13}}{4}$ for $x_{2}$.
