(6x-6)/(x^2-2)=3

Solution for (6x-6)/(x^2-2)=3 equation:

(6x-6)/(x^2-2)=3

We move all terms to the left:

(6x-6)/(x^2-2)-(3)=0


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

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

x^2!=2

x^2!=2/

x^2!=√1/0

x!=1

x∈R


We multiply all the terms by the denominator


(6x-6)-3*(x^2-2)=0

We multiply parentheses

-3x^2+(6x-6)+6=0

We get rid of parentheses

-3x^2+6x-6+6=0

We add all the numbers together, and all the variables

-3x^2+6x=0

a = -3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-3)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-3}=\frac{0}{-6}
=0
$