# How do you solve 6x^2 - x - 5 = 0  using the quadratic formula?

Aug 10, 2015

#### Answer:

The solutions for the equation are

color(blue)(x=1, x=-5/6

#### Explanation:

6x^2−x−5=0

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

The Discriminant is given by:

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

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

$= 1 + 120$

$= 121$

The solutions are found using the formula

$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(- 1\right) \pm \sqrt{121}}{2 \cdot 6} = \frac{1 \pm 11}{12}$

x = -10/12, color(blue)(x=-5/6

x=12/12, color(blue)(x=1