(x^2-4x-12)/(x+6)=0

Solution for (x^2-4x-12)/(x+6)=0 equation:

(x^2-4x-12)/(x+6)=0


Domain of the equation: (x+6)!=0

We move all terms containing x to the left, all other terms to the right

x!=-6

x∈R


We multiply all the terms by the denominator


(x^2-4x-12)=0

We get rid of parentheses

x^2-4x-12=0

a = 1; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*1}=\frac{12}{2}
=6
$