3/5n+15=10+2/n

Solution for 3/5n+15=10+2/n equation:

3/5n+15=10+2/n

We move all terms to the left:

3/5n+15-(10+2/n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3/5n-(2/n+10)+15=0

We get rid of parentheses

3/5n-2/n-10+15=0

We calculate fractions


3n/5n^2+(-10n)/5n^2-10+15=0

We add all the numbers together, and all the variables

3n/5n^2+(-10n)/5n^2+5=0

We multiply all the terms by the denominator


3n+(-10n)+5*5n^2=0

Wy multiply elements

25n^2+3n+(-10n)=0

We get rid of parentheses

25n^2+3n-10n=0

We add all the numbers together, and all the variables

25n^2-7n=0

a = 25; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·25·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*25}=\frac{0}{50}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*25}=\frac{14}{50}
=7/25
$