n/3*n=2*9

Solution for n/3*n=2*9 equation:

n/3*n=2*9

We move all terms to the left:

n/3*n-(2*9)=0


Domain of the equation: 3*n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

n/3*n-18=0

We multiply all the terms by the denominator


n-18*3*n=0

Wy multiply elements

n-54n*n=0

Wy multiply elements

-54n^2+n=0

a = -54; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-54)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-54}=\frac{-2}{-108}
=1/54
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-54}=\frac{0}{-108}
=0
$