# How do you find the value of the discriminant and state the type of solutions given -2x^2-8x-14=-6?

Determinant $= 0$ & the roots are real & equal

#### Explanation:

$- 2 {x}^{2} - 8 x - 14 = - 6$

${x}^{2} + 4 x + 4 = 0$

Comparing the above equation with the standard form of quadratic equation: $a {x}^{2} + b x + c = 0$, we get

$a = 1 , b = 4 , c = 4$

hence the determinant is given as

${b}^{2} - 4 a c = {4}^{2} - 4 \left(1\right) \left(4\right) = 0$

Since ${b}^{2} - 4 a c = 0$ the roots are real & equal.