# What is the solution set for x^2 - 5x + 6 = 0?

Aug 31, 2015

${x}_{1 , 2} = \frac{5 \pm 1}{2}$

#### Explanation:

For a general form quadratic equation

$\textcolor{b l u e}{a {x}^{2} + b x + c = 0}$

you can determine its roots by using the quadratic formula

$\textcolor{b l u e}{{x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}}$

In your case, $a = 1$, $b = - 5$, and $c = 6$. This means that you have

${x}_{1 , 2} = \frac{- \left(- 5\right) \pm \sqrt{{\left(- 5\right)}^{2} - 4 \cdot 1 \cdot 6}}{2 \cdot 1}$

${x}_{1 , 2} = \frac{5 \pm \sqrt{1}}{2}$

${x}_{1 , 2} = \frac{5 \pm 1}{2}$

The two roots will thus be

${x}_{1} = \frac{5 + 1}{2} = \textcolor{g r e e n}{3} \text{ }$ and $\text{ } {x}_{2} = \frac{5 - 1}{2} = \textcolor{g r e e n}{2}$