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

Mar 8, 2016

$x = \frac{- 8 \pm 2 \sqrt{- 19}}{14}$

#### Explanation:

The quadratic formula states that the solutions to a quadratic of the form $a {x}^{2} + b x + c = 0$ are given by

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

So in this case

$x = \frac{- 8 \pm \sqrt{{8}^{2} - 4 \cdot 7 \cdot 5}}{2 \cdot 7}$

$= \frac{- 8 \pm \sqrt{64 - 140}}{14} = \frac{- 8 \pm \sqrt{- 76}}{14} = \frac{- 8 \pm 2 \sqrt{- 19}}{14}$

This has only imaginary solutions.