X^2-12x-16=-2

Solution for X^2-12x-16=-2 equation:

X^2-12X-16=-2

We move all terms to the left:

X^2-12X-16-(-2)=0

We add all the numbers together, and all the variables

X^2-12X-14=0

a = 1; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·1·(-14)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{2}}{2*1}=\frac{12-10\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{2}}{2*1}=\frac{12+10\sqrt{2}}{2}
$