3n+15/n=-30

Solution for 3n+15/n=-30 equation:

3n+15/n=-30

We move all terms to the left:

3n+15/n-(-30)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

3n+15/n+30=0

We multiply all the terms by the denominator


3n*n+30*n+15=0

We add all the numbers together, and all the variables

30n+3n*n+15=0

Wy multiply elements

3n^2+30n+15=0

a = 3; b = 30; c = +15;
Δ = b2-4ac
Δ = 302-4·3·15
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{5}}{2*3}=\frac{-30-12\sqrt{5}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{5}}{2*3}=\frac{-30+12\sqrt{5}}{6}
$