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

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

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

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n+1)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


(-9n)/24n^2+8n/24n^2+9n/24n^2-1=0

We multiply all the terms by the denominator


(-9n)+8n+9n-1*24n^2=0

We add all the numbers together, and all the variables

17n+(-9n)-1*24n^2=0

Wy multiply elements

-24n^2+17n+(-9n)=0

We get rid of parentheses

-24n^2+17n-9n=0

We add all the numbers together, and all the variables

-24n^2+8n=0

a = -24; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-24)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-24}=\frac{-16}{-48}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-24}=\frac{0}{-48}
=0
$