2+4/3x=11-1/6x

Solution for 2+4/3x=11-1/6x equation:

2+4/3x=11-1/6x

We move all terms to the left:

2+4/3x-(11-1/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-1/6x+11)+2=0

We get rid of parentheses

4/3x+1/6x-11+2=0

We calculate fractions


24x/18x^2+3x/18x^2-11+2=0

We add all the numbers together, and all the variables

24x/18x^2+3x/18x^2-9=0

We multiply all the terms by the denominator


24x+3x-9*18x^2=0

We add all the numbers together, and all the variables

27x-9*18x^2=0

Wy multiply elements

-162x^2+27x=0

a = -162; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-162)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-162}=\frac{-54}{-324}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-162}=\frac{0}{-324}
=0
$