# How do you solve x^2 - 2x - 3 = 0 using the quadratic formula?

Jun 12, 2015

the solutions are
 color(green)(x= 3
 color(green)( x=-1

#### Explanation:

${x}^{2} - 2 x - 3 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 2 , c = - 3$

The Discriminant is given by:
$\Delta = {b}^{2} - \left(4 \cdot a \cdot c\right)$

$= {\left(- 2\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 3\right)\right)$
$= 4 + 12 = 16$

As $\Delta > 0$ there are two solutions,

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

As $\Delta = 16$, $x = \frac{- \left(- 2\right) \pm \sqrt{16}}{2 \cdot 1} = \frac{2 \pm 4}{2}$

the solutions are
 color(green)(x= 6/2 = 3
 color(green)( x=-2/2=-1