# How do you solve 2x^2 + 9x + 4 = 0 using the quadratic formula?

Feb 27, 2016

$x = \frac{- 1}{2} \mathmr{and} x = - 4$

#### Explanation:

Given equation is $2 {x}^{2} + 9 x + 4 = 0$
Comparing with $a {x}^{2} + b x + c = 0$

We get, a= 2; b=9, c= 4

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{- 9 \pm \sqrt{{9}^{2} - 4 \times 2 \times 4}}{2 \times 2}$

$x = \frac{- 9 \pm \sqrt{81 - 32}}{4}$

$x = \frac{- 9 \pm \sqrt{49}}{4}$

$x = \frac{- 9 \pm 7}{4}$

$x = \frac{- 9 + 7}{4} \mathmr{and} x = \frac{- 9 - 7}{4}$

$x = \frac{- 2}{4} \mathmr{and} x = \frac{- 16}{4}$

$x = \frac{- 1}{2} \mathmr{and} x = - 4$