# How do you solve 2x^2-x= -5 using the quadratic formula?

Apr 26, 2016

The solutions for the equation are:

color(green)( x = (1+sqrt(-39))/4, color(green)( x = (1-sqrt(-39))/4

#### Explanation:

$2 {x}^{2} - x = - 5$

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

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

The Discriminant is given by:

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

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

$= 1 - 40 = - 39$

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

$x = \frac{- \left(- 1\right) \pm \sqrt{- 39}}{2 \cdot 2} = \frac{1 \pm \sqrt{- 39}}{4}$

The solutions are:

• color(green)( x = (1+sqrt(-39))/4

• color(green)( x = (1-sqrt(-39))/4