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

Oct 21, 2015

The solutions are
x=color(blue)((-8+sqrt(-76))/10
x=color(blue)((-8-sqrt(-76))/10

Explanation:

$5 {x}^{2} + 8 x + 7 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 5 , b = 8 , c = 7$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(8\right)}^{2} - \left(4 \cdot 5 \cdot 7\right)$

$= 64 - 140 = - 76$

The solutions are normally found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(8\right) \pm \sqrt{- 76}}{2 \cdot 5} = \frac{- 8 \pm \sqrt{- 76}}{10}$

The solutions are
x=color(blue)((-8+sqrt(-76))/10
x=color(blue)((-8-sqrt(-76))/10