11/6x-12/4=4/3x

Solution for 11/6x-12/4=4/3x equation:

11/6x-12/4=4/3x

We move all terms to the left:

11/6x-12/4-(4/3x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

11/6x-(+4/3x)-12/4=0

We add all the numbers together, and all the variables

11/6x-(+4/3x)-3=0

We get rid of parentheses

11/6x-4/3x-3=0

We calculate fractions


33x/18x^2+(-24x)/18x^2-3=0

We multiply all the terms by the denominator


33x+(-24x)-3*18x^2=0

Wy multiply elements

-54x^2+33x+(-24x)=0

We get rid of parentheses

-54x^2+33x-24x=0

We add all the numbers together, and all the variables

-54x^2+9x=0

a = -54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-54)·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*-54}=\frac{-18}{-108}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-54}=\frac{0}{-108}
=0
$