2+3n=4/5n+15

Solution for 2+3n=4/5n+15 equation:

2+3n=4/5n+15

We move all terms to the left:

2+3n-(4/5n+15)=0


Domain of the equation: 5n+15)!=0

n∈R


We get rid of parentheses

3n-4/5n-15+2=0

We multiply all the terms by the denominator


3n*5n-15*5n+2*5n-4=0

Wy multiply elements

15n^2-75n+10n-4=0

We add all the numbers together, and all the variables

15n^2-65n-4=0

a = 15; b = -65; c = -4;
Δ = b2-4ac
Δ = -652-4·15·(-4)
Δ = 4465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{4465}}{2*15}=\frac{65-\sqrt{4465}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4465}}{2*15}=\frac{65+\sqrt{4465}}{30}
$