1/3*n=3

Solution for 1/3*n=3 equation:

1/3*n=3

We move all terms to the left:

1/3*n-(3)=0


Domain of the equation: 3*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-3*3*n+1=0

Wy multiply elements

-9n*n+1=0

Wy multiply elements

-9n^2+1=0

a = -9; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-9)·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-9}=\frac{-6}{-18}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-9}=\frac{6}{-18}
=-1/3
$