15-1/3n=1/6n-1

Solution for 15-1/3n=1/6n-1 equation:

15-1/3n=1/6n-1

We move all terms to the left:

15-1/3n-(1/6n-1)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 6n-1)!=0

n∈R


We get rid of parentheses

-1/3n-1/6n+1+15=0

We calculate fractions


(-6n)/18n^2+(-3n)/18n^2+1+15=0

We add all the numbers together, and all the variables

(-6n)/18n^2+(-3n)/18n^2+16=0

We multiply all the terms by the denominator


(-6n)+(-3n)+16*18n^2=0

Wy multiply elements

288n^2+(-6n)+(-3n)=0

We get rid of parentheses

288n^2-6n-3n=0

We add all the numbers together, and all the variables

288n^2-9n=0

a = 288; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·288·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*288}=\frac{0}{576}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*288}=\frac{18}{576}
=1/32
$