# How do you solve 7x^2+5x+8=0 using the quadratic formula?

Jul 31, 2016

No real roots.

#### Explanation:

Use the new quadratic formula in graphic form (Socratic Search)
y = 7x^2 + 5x + 8 = 0
D = d^2 = b^2 - 4ac = 25 - 224 = - 199 < 0
Because D < 0, there are no real roots.

Note. There are 2 complex roots. $d = \pm i \sqrt{199}$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{5}{14} \pm \frac{i \sqrt{199}}{14} = \frac{- 5 \pm i \sqrt{199}}{14}$