15/5+3n=9/n

Solution for 15/5+3n=9/n equation:

15/5+3n=9/n

We move all terms to the left:

15/5+3n-(9/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3n-(+9/n)+15/5=0

We add all the numbers together, and all the variables

3n-(+9/n)+3=0

We get rid of parentheses

3n-9/n+3=0

We multiply all the terms by the denominator


3n*n+3*n-9=0

We add all the numbers together, and all the variables

3n+3n*n-9=0

Wy multiply elements

3n^2+3n-9=0

a = 3; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·3·(-9)
Δ = 117
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{13}}{2*3}=\frac{-3-3\sqrt{13}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{13}}{2*3}=\frac{-3+3\sqrt{13}}{6}
$