6x/3x-1-6/x-2=2

Solution for 6x/3x-1-6/x-2=2 equation:

6x/3x-1-6/x-2=2

We move all terms to the left:

6x/3x-1-6/x-2-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

6x/3x-6/x-5=0

We calculate fractions


6x^2/3x^2+(-18x)/3x^2-5=0

We multiply all the terms by the denominator


6x^2+(-18x)-5*3x^2=0

Wy multiply elements

6x^2-15x^2+(-18x)=0

We get rid of parentheses

6x^2-15x^2-18x=0

We add all the numbers together, and all the variables

-9x^2-18x=0

a = -9; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-9)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-9}=\frac{36}{-18}
=-2
$