# How do you solve x^2-5x+6=0 ?

Apr 19, 2016

The solutions are
color(blue)( x= 3

color(blue)( x = 2

#### Explanation:

${x}^{2} - 5 x + 6 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 5 , c = 6$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 5\right)}^{2} - \left(4 \cdot 1 \cdot 6\right)$

$= 25 - 24 = 1$

The solutions are normally found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

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

color(blue)( x = ( 5 +1)/2 = 6/2 = 3

color(blue)( x = ( 5 -1)/2 = 4 /2 = 2