# How do you solve 2x^2-x-4=0 using the quadratic formula?

Jul 25, 2015

The solutions are:
color(blue)(x=(1+sqrt(33))/4 , x=(1-sqrt(33))/4

#### Explanation:

The equation 2x^2−x−4 : is of the form color(blue)(ax^2+bx+c=0 where:

$a = 2 , b = - 1 , c = - 4$

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

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

$= 1 + 32$
$= 33$

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

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

$x = \frac{- \left(- 1\right) \pm \sqrt{33}}{2 \cdot 2} = \frac{1 \pm \sqrt{33}}{4}$
The solutions are:
color(blue)(x=(1+sqrt(33))/4 , x=(1-sqrt(33))/4