# How do you solve 11x^2-x-3=0 using the quadratic formula?

Aug 10, 2015

The solutions for the equation are:
color(blue)( x =(1+sqrt(133))/22
color(blue)( x =(1-sqrt(133))/22

#### Explanation:

11x^2−x−3 =0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 11 , b = - 1 , c = - 3$

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

$= {\left(- 1\right)}^{2} - \left(4 \cdot 11 \cdot \left(- 3\right)\right)$

$= 133$

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

$x = \frac{- \left(- 1\right) \pm \sqrt{133}}{2 \cdot 11} = \frac{1 \pm \sqrt{133}}{22}$

The solutions are:
color(blue)( x =(1+sqrt(133))/22
color(blue)( x =(1-sqrt(133))/22