2/3x-2=6+11/12x

Solution for 2/3x-2=6+11/12x equation:

2/3x-2=6+11/12x

We move all terms to the left:

2/3x-2-(6+11/12x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(11/12x+6)-2=0

We get rid of parentheses

2/3x-11/12x-6-2=0

We calculate fractions


24x/36x^2+(-33x)/36x^2-6-2=0

We add all the numbers together, and all the variables

24x/36x^2+(-33x)/36x^2-8=0

We multiply all the terms by the denominator


24x+(-33x)-8*36x^2=0

Wy multiply elements

-288x^2+24x+(-33x)=0

We get rid of parentheses

-288x^2+24x-33x=0

We add all the numbers together, and all the variables

-288x^2-9x=0

a = -288; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-288)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-288}=\frac{0}{-576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-288}=\frac{18}{-576}
=-1/32
$