-5/3n+3/2n=5/8

Solution for -5/3n+3/2n=5/8 equation:

-5/3n+3/2n=5/8

We move all terms to the left:

-5/3n+3/2n-(5/8)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-5/3n+3/2n-(+5/8)=0

We get rid of parentheses

-5/3n+3/2n-5/8=0

We calculate fractions


(-60n^2)/384n^2+(-640n)/384n^2+576n/384n^2=0

We multiply all the terms by the denominator


(-60n^2)+(-640n)+576n=0

We add all the numbers together, and all the variables

(-60n^2)+576n+(-640n)=0

We get rid of parentheses

-60n^2+576n-640n=0

We add all the numbers together, and all the variables

-60n^2-64n=0

a = -60; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·(-60)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*-60}=\frac{0}{-120}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*-60}=\frac{128}{-120}
=-1+1/15
$