# How do you evaluate sqrt(b^2-4ac) for a=2, b=-4, c=-6?

Dec 19, 2016

The discriminant $D = {\left(- 4\right)}^{2} - 4 \cdot 2 \cdot \left(- 6\right)$

#### Explanation:

$D = 16 - \left(- 48\right) = 16 + 48 = 64$ This is $> 0$
so there will be two solutions to the equation $2 {x}^{2} - 4 x - 6 = 0$

The square root $\sqrt{D} = \sqrt{64} = 8$

The two solutions being:

${x}_{1 , 2} = \frac{- b \pm \sqrt{D}}{2 a} = \frac{+ 4 \pm 8}{4} = 1 \pm 2$

$\to x = + 3 \mathmr{and} x = - 1$