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

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

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

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 6n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

27n-9*18n^2=0

Wy multiply elements

-162n^2+27n=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:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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