2/3x-3/4=11/12x

Solution for 2/3x-3/4=11/12x equation:

2/3x-3/4=11/12x

We move all terms to the left:

2/3x-3/4-(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)-3/4=0

We get rid of parentheses

2/3x-11/12x-3/4=0

We calculate fractions


(-108x^2)/576x^2+384x/576x^2+(-528x)/576x^2=0

We multiply all the terms by the denominator


(-108x^2)+384x+(-528x)=0

We get rid of parentheses

-108x^2+384x-528x=0

We add all the numbers together, and all the variables

-108x^2-144x=0

a = -108; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-108)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-108}=\frac{288}{-216}
=-1+1/3
$