3n/n=2n

Solution for 3n/n=2n equation:

3n/n=2n

We move all terms to the left:

3n/n-(2n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-2n+3n/n=0

We multiply all the terms by the denominator


-2n*n+3n=0

We add all the numbers together, and all the variables

3n-2n*n=0

Wy multiply elements

-2n^2+3n=0

a = -2; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-2)·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*-2}=\frac{-6}{-4}
=1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-2}=\frac{0}{-4}
=0
$