5/2n=8/3n-12

Solution for 5/2n=8/3n-12 equation:

5/2n=8/3n-12

We move all terms to the left:

5/2n-(8/3n-12)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n-12)!=0

n∈R


We get rid of parentheses

5/2n-8/3n+12=0

We calculate fractions


15n/6n^2+(-16n)/6n^2+12=0

We multiply all the terms by the denominator


15n+(-16n)+12*6n^2=0

Wy multiply elements

72n^2+15n+(-16n)=0

We get rid of parentheses

72n^2+15n-16n=0

We add all the numbers together, and all the variables

72n^2-1n=0

a = 72; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·72·0
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*72}=\frac{0}{144}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*72}=\frac{2}{144}
=1/72
$