# How do you solve 5x^2+9x-2=0 using the quadratic formula?

Jul 25, 2015

The solutions for the equation are:
color(blue)(x=-2,x=1/5

#### Explanation:

The equation 5x^2+9x−2 is of the form color(blue)(ax^2+bx+c=0 where:
$a = 5 , b = 9 , c = - 2$

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

$= {\left(9\right)}^{2} - \left(4\right) \cdot \left(5\right) \cdot \left(- 2\right)$

$= 81 + 40 = 121$

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

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

As $\Delta = 121$, $x = \frac{\left(- 9\right) \pm \sqrt{121}}{2 \cdot 5} = \frac{- 9 \pm 11}{10}$

x=((-9-11)/10) = -20/10 =color(blue)( -2

x=((-9+11)/10) = 2/10 =color(blue)( 1/5