# How do you find the value of the discriminant and state the type of solutions given -x^2-9=6x?

Nov 15, 2017

Solution: $x = - 3$

#### Explanation:

$- {x}^{2} - 9 = 6 x \mathmr{and} - {x}^{2} - 6 x - 9 = 0$

Comparing with standard quadratic equation $a {x}^{2} + b x + c = 0$

$a = - 1 , b = - 6 , c = - 9$ Discriminant $D = {b}^{2} - 4 a c$ or

$D = 36 - 36 = 0$ If discriminant positive, we get two real solutions,

if it is zero we get just one solution, and if it is negative we get

complex solutions. Discriminant is zero , so it has one root .

Quadratic formula: $x = \frac{- b \pm \sqrt{D}}{2 a}$or

$x = \frac{6 \pm \sqrt{0}}{- 2} = - 3$

Solution: $x = - 3$ [Ans]