# How do you solve the quadratic using the quadratic formula given 8a^2+6a=-5?

Sep 26, 2017

Solution: $x \approx - 0.375 + 0.69597 i , x \approx - 0.375 - 0.69597 i$

#### Explanation:

$8 {a}^{2} + 6 a = - 5 \mathmr{and} 8 {a}^{2} + 6 a + 5 = 0$ Comparing with standard

quadratic equation $a {x}^{2} + b x + c = 0$ we get  a=8 ;b=6 ,c=5

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

Discriminant $D = {b}^{2} - 4 a c = - 124$ is negative , so it has

complex roots .

$x = \frac{- 6 \pm \sqrt{{\left(- 6\right)}^{2} - 4 \cdot 8 \cdot 5}}{2 \cdot 8} = \frac{- 6 \pm \sqrt{- 124}}{2 \cdot 8}$

$x = - \frac{3}{8} \pm \frac{\cancel{2} \sqrt{31} i}{\cancel{2} \cdot 8} = - \frac{3}{8} \pm \frac{\sqrt{31}}{8} i$

$\therefore x = - \frac{3}{8} + \frac{\sqrt{31}}{8} i , - \frac{3}{8} - \frac{\sqrt{31}}{8} i$ or Solution:

$x \approx - 0.375 + 0.69597 i , x \approx - 0.375 - 0.69597 i$