3/2n+5/3n=-133/36

Solution for 3/2n+5/3n=-133/36 equation:

3/2n+5/3n=-133/36

We move all terms to the left:

3/2n+5/3n-(-133/36)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

3/2n+5/3n+133/36=0

We calculate fractions


2394n^2/648n^2+972n/648n^2+1080n/648n^2=0

We multiply all the terms by the denominator


2394n^2+972n+1080n=0

We add all the numbers together, and all the variables

2394n^2+2052n=0

a = 2394; b = 2052; c = 0;
Δ = b2-4ac
Δ = 20522-4·2394·0
Δ = 4210704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4210704}=2052$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2052)-2052}{2*2394}=\frac{-4104}{4788}
=-6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2052)+2052}{2*2394}=\frac{0}{4788}
=0
$