# How do you solve 6x^2+3x-15=0 using the quadratic formula?

Aug 10, 2015

The solutions for the equation are :
color(blue)( x=(-3+sqrt(369))/12

color(blue)( x=(-3-sqrt(369))/12

#### Explanation:

 6x^2+3x−15=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 6 , b = 3 , c = - 15$

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

$= {\left(3\right)}^{2} - \left(4 \cdot 6 \cdot - \left(15\right)\right)$

$= 9 + 360 = 369$

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

$x = \frac{\left(- 3\right) \pm \sqrt{369}}{2 \cdot 6} = \frac{- 3 \pm \sqrt{369}}{12}$

The solutions for the equation are :
color(blue)( x=(-3+sqrt(369))/12

color(blue)( x=(-3-sqrt(369))/12