2/3n+1/6=1/2n=1/2

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

2/3n+1/6=1/2n=1/2

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


12n^2/216n^2+144n/216n^2+(-108n)/216n^2=0

We multiply all the terms by the denominator


12n^2+144n+(-108n)=0

We get rid of parentheses

12n^2+144n-108n=0

We add all the numbers together, and all the variables

12n^2+36n=0

a = 12; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·12·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*12}=\frac{-72}{24}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*12}=\frac{0}{24}
=0
$