x^2-12x-90=-6

Solution for x^2-12x-90=-6 equation:

x^2-12x-90=-6

We move all terms to the left:

x^2-12x-90-(-6)=0

We add all the numbers together, and all the variables

x^2-12x-84=0

a = 1; b = -12; c = -84;
Δ = b2-4ac
Δ = -122-4·1·(-84)
Δ = 480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{30}}{2*1}=\frac{12-4\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{30}}{2*1}=\frac{12+4\sqrt{30}}{2}
$