5/2n=8/3n-5

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

5/2n=8/3n-5

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n-5)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


15n/6n^2+(-16n)/6n^2+5=0

We multiply all the terms by the denominator


15n+(-16n)+5*6n^2=0

Wy multiply elements

30n^2+15n+(-16n)=0

We get rid of parentheses

30n^2+15n-16n=0

We add all the numbers together, and all the variables

30n^2-1n=0

a = 30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·30·0
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*30}=\frac{0}{60}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*30}=\frac{2}{60}
=1/30
$