# How do you solve 2x^2+3x-4=0 using the quadratic formula?

Dec 7, 2016

$x = \frac{- 3 + \sqrt{41}}{4} ,$ $\frac{- 3 - \sqrt{41}}{4}$

#### Explanation:

$2 {x}^{2} + 3 x - 4 = 0$ is a quadratic equation in the form $a {x}^{2} + b x + c$, where $a = 2$, $b = 3$, and $c = - 4$.

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

Plug the known values into the equation and solve.

$x = \frac{- 3 \pm \sqrt{{3}^{2} - 4 \cdot 2 \cdot - 4}}{2 \cdot 2}$

$x = \frac{- 3 \pm \sqrt{9 + 32}}{4}$

$x = \frac{- 3 \pm \sqrt{41}}{4}$

$x = \frac{- 3 + \sqrt{41}}{4} ,$ $\frac{- 3 - \sqrt{41}}{4}$