# How do you solve x^2-5x+3=0?

Apr 2, 2016

Use the quadratic formula to find roots:

$x = \frac{5}{2} \pm \frac{\sqrt{13}}{2}$

#### Explanation:

This quadratic equation is in the form $a {x}^{2} + b x + c = 0$ with $a = 1$, $b = - 5$ and $c = 3$.

It has roots given by the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$= \frac{5 \pm \sqrt{{5}^{2} - \left(4 \cdot 1 \cdot 3\right)}}{2 \cdot 1}$

$= \frac{5 \pm \sqrt{25 - 12}}{2}$

$= \frac{5 \pm \sqrt{13}}{2}$

That is $x = \frac{5}{2} + \frac{\sqrt{13}}{2}$ or $x = \frac{5}{2} - \frac{\sqrt{13}}{2}$