# How do you solve d^2+5d+6=0 using the quadratic formula?

Aug 10, 2015

The solutions for the equation are:
color(blue)(x=-2

color(blue)(x=-3

#### Explanation:

${d}^{2} + 5 d + 6 = 0$

The equation is of the form color(blue)(ad^2+bd+c=0 where:

$a = 1 , b = 5 , c = 6$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(5\right)}^{2} - \left(4 \cdot 1 \cdot 6\right)$

$= 25 - 24 = 1$

As $\Delta = 0$ there is only one solution.

The solutions are found using the formula:

$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 5\right) \pm \sqrt{1}}{2 \cdot 1} = \frac{- 5 \pm 1}{2}$

The solutions for the equation are:
x =(-5+1)/2 , x=-4/2,color(blue)(x=-2

x =(-5-1)/2 , x=-6/2,color(blue)(x=-3