(X)=-x2-8x-12

Solution for (X)=-x2-8x-12 equation:

(X)=-X2-8X-12

We move all terms to the left:

(X)-(-X2-8X-12)=0

We add all the numbers together, and all the variables

-(-1X^2-8X-12)+X=0

We get rid of parentheses

1X^2+8X+X+12=0

We add all the numbers together, and all the variables

X^2+9X+12=0

a = 1; b = 9; c = +12;
Δ = b2-4ac
Δ = 92-4·1·12
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{33}}{2*1}=\frac{-9-\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*1}=\frac{-9+\sqrt{33}}{2}
$