(x^2-6x+9)/(x^2-9)=-2

Solution for (x^2-6x+9)/(x^2-9)=-2 equation:

(x^2-6x+9)/(x^2-9)=-2

We move all terms to the left:

(x^2-6x+9)/(x^2-9)-(-2)=0


Domain of the equation: (x^2-9)!=0

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

x^2!=9

x^2!=9/

x^2!=√1/0

x!=1

x∈R


We add all the numbers together, and all the variables

(x^2-6x+9)/(x^2-9)+2=0

We multiply all the terms by the denominator


(x^2-6x+9)+2*(x^2-9)=0

We multiply parentheses

2x^2+(x^2-6x+9)-18=0

We get rid of parentheses

2x^2+x^2-6x+9-18=0

We add all the numbers together, and all the variables

3x^2-6x-9=0

a = 3; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·3·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*3}=\frac{18}{6}
=3
$