-x^2-12x-6=21

Solution for -x^2-12x-6=21 equation:

-x^2-12x-6=21

We move all terms to the left:

-x^2-12x-6-(21)=0

We add all the numbers together, and all the variables

-1x^2-12x-27=0

a = -1; b = -12; c = -27;
Δ = b2-4ac
Δ = -122-4·(-1)·(-27)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6}{2*-1}=\frac{6}{-2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6}{2*-1}=\frac{18}{-2}
=-9
$