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

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

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

We move all terms to the left:

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-18n^2+6n-3n=0

We add all the numbers together, and all the variables

-18n^2+3n=0

a = -18; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-18)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-18}=\frac{-6}{-36}
=1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-18}=\frac{0}{-36}
=0
$