1/3n-1/9=1/6n

Solution for 1/3n-1/9=1/6n equation:

1/3n-1/9=1/6n

We move all terms to the left:

1/3n-1/9-(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

1/3n-(+1/6n)-1/9=0

We get rid of parentheses

1/3n-1/6n-1/9=0

We calculate fractions


(-108n^2)/1458n^2+486n/1458n^2+(-243n)/1458n^2=0

We multiply all the terms by the denominator


(-108n^2)+486n+(-243n)=0

We get rid of parentheses

-108n^2+486n-243n=0

We add all the numbers together, and all the variables

-108n^2+243n=0

a = -108; b = 243; c = 0;
Δ = b2-4ac
Δ = 2432-4·(-108)·0
Δ = 59049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{59049}=243$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(243)-243}{2*-108}=\frac{-486}{-216}
=2+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(243)+243}{2*-108}=\frac{0}{-216}
=0
$