(6n^2+3n)/3n=0

Solution for (6n^2+3n)/3n=0 equation:

(6n^2+3n)/3n=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We multiply all the terms by the denominator


(6n^2+3n)=0

We get rid of parentheses

6n^2+3n=0

a = 6; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·6·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*6}=\frac{-6}{12}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*6}=\frac{0}{12}
=0
$