# How do you solve 2x^2 + 8x - 3 = 0 using the quadratic formula?

Aug 6, 2016

$x = 2 - \frac{\sqrt{22}}{2}$ or $x = 2 + \frac{\sqrt{22}}{2}$

#### Explanation:

Quadratic formula gives the solution of quadratic equation $a {x}^{2} + b x + c = 0$ as $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

Hence solution of $2 {x}^{2} + 8 x - 3 = 0$ using the formula is given by

$x = \frac{- 8 \pm \sqrt{{8}^{2} - 4 \times 2 \times \left(- 3\right)}}{2 \times 2}$ or

$x = \frac{- 8 \pm \sqrt{64 + 24}}{4}$ or

$x = \frac{- 8 \pm \sqrt{88}}{4}$ or

$x = - 2 \pm \frac{\sqrt{4 \times 22}}{4} = 2 \pm \frac{2}{4} \sqrt{22}$ or

$x = 2 \pm \frac{\sqrt{22}}{2}$ i.e.

$x = 2 - \frac{\sqrt{22}}{2}$ or $x = 2 + \frac{\sqrt{22}}{2}$