3n/2n-1=n

Solution for 3n/2n-1=n equation:

3n/2n-1=n

We move all terms to the left:

3n/2n-1-(n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+3n/2n-1=0

We multiply all the terms by the denominator


-1n*2n+3n-1*2n=0

We add all the numbers together, and all the variables

3n-1n*2n-1*2n=0

Wy multiply elements

-2n^2+3n-2n=0

We add all the numbers together, and all the variables

-2n^2+n=0

a = -2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-2)·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*-2}=\frac{-2}{-4}
=1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-2}=\frac{0}{-4}
=0
$