# How do you solve the quadratic using the quadratic formula given x^2-4x-7=0?

Aug 9, 2017

$x = 5.31662479 \vee x = - 1.31662479$

#### Explanation:

${x}^{2} - 4 x - 7 = 0$
First you calculate the discriminant.

$D = {\left(- 4\right)}^{2} - 4 \cdot 1 \cdot - 7 = 16 + 28 = 44$ ($D = {b}^{2} - 4 \cdot a \cdot c$)

Then you use the general formula $x = \frac{- b \pm \sqrt{D}}{2 a}$

Which gives: $x = \frac{4 \pm \sqrt{44}}{2 \cdot 1} = x = 5.31662479 \vee x = - 1.31662479$