1/3n+80=1/2n+120

Solution for 1/3n+80=1/2n+120 equation:

1/3n+80=1/2n+120

We move all terms to the left:

1/3n+80-(1/2n+120)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n+120)!=0

n∈R


We get rid of parentheses

1/3n-1/2n-120+80=0

We calculate fractions


2n/6n^2+(-3n)/6n^2-120+80=0

We add all the numbers together, and all the variables

2n/6n^2+(-3n)/6n^2-40=0

We multiply all the terms by the denominator


2n+(-3n)-40*6n^2=0

Wy multiply elements

-240n^2+2n+(-3n)=0

We get rid of parentheses

-240n^2+2n-3n=0

We add all the numbers together, and all the variables

-240n^2-1n=0

a = -240; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-240)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-240}=\frac{0}{-480}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-240}=\frac{2}{-480}
=-1/240
$