(x^2-11x-12)/(x+1)=2

Solution for (x^2-11x-12)/(x+1)=2 equation:

(x^2-11x-12)/(x+1)=2

We move all terms to the left:

(x^2-11x-12)/(x+1)-(2)=0


Domain of the equation: (x+1)!=0

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

x!=-1

x∈R


We multiply all the terms by the denominator


(x^2-11x-12)-2*(x+1)=0

We multiply parentheses

(x^2-11x-12)-2x-2=0

We get rid of parentheses

x^2-11x-2x-12-2=0

We add all the numbers together, and all the variables

x^2-13x-14=0

a = 1; b = -13; c = -14;
Δ = b2-4ac
Δ = -132-4·1·(-14)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-15}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+15}{2*1}=\frac{28}{2}
=14
$