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

Mar 20, 2016

#### Explanation:

Mar 20, 2016

$x = \frac{1}{5} , - 2$

#### Explanation:

color(blue)(5x^2+9x-2=0

This is a Quadratic equation (in form $a {x}^{2} + b x + c = 0$)

color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)

Where

color(red)(a=5,b=9,c=-2

Substitute the values

$\rightarrow x = \frac{- 9 \pm \sqrt{{9}^{2} - 4 \left(5\right) \left(- 2\right)}}{2 \left(5\right)}$

$\rightarrow x = \frac{- 9 \pm \sqrt{81 - 4 \left(5\right) \left(- 2\right)}}{10}$

$\rightarrow x = \frac{- 9 \pm \sqrt{81 - \left(- 40\right)}}{10}$

$\rightarrow x = \frac{- 9 \pm \sqrt{81 + 40}}{10}$

$\rightarrow x = \frac{- 9 \pm \sqrt{121}}{10}$

$\Rightarrow x = \frac{- 9 \pm 11}{10}$

Now we have $2$ solutions

color(orange)(rArrx=(-9+11)/(10)=2/10=1/5

color(indigo)(rArrx=(-9-11)/(10)=-20/10=-2

color(green)( ul bar|:.x=1/5,-2|