91/36+3/4n=5/3n+1

Solution for 91/36+3/4n=5/3n+1 equation:

91/36+3/4n=5/3n+1

We move all terms to the left:

91/36+3/4n-(5/3n+1)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n+1)!=0

n∈R


We get rid of parentheses

3/4n-5/3n-1+91/36=0

We calculate fractions


3276n^2/1296n^2+972n/1296n^2+(-2160n)/1296n^2-1=0

We multiply all the terms by the denominator


3276n^2+972n+(-2160n)-1*1296n^2=0

Wy multiply elements

3276n^2-1296n^2+972n+(-2160n)=0

We get rid of parentheses

3276n^2-1296n^2+972n-2160n=0

We add all the numbers together, and all the variables

1980n^2-1188n=0

a = 1980; b = -1188; c = 0;
Δ = b2-4ac
Δ = -11882-4·1980·0
Δ = 1411344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1411344}=1188$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1188)-1188}{2*1980}=\frac{0}{3960}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1188)+1188}{2*1980}=\frac{2376}{3960}
=3/5
$