6+1/2n=4+1/3n

Solution for 6+1/2n=4+1/3n equation:

6+1/2n=4+1/3n

We move all terms to the left:

6+1/2n-(4+1/3n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/2n-(1/3n+4)+6=0

We get rid of parentheses

1/2n-1/3n-4+6=0

We calculate fractions


3n/6n^2+(-2n)/6n^2-4+6=0

We add all the numbers together, and all the variables

3n/6n^2+(-2n)/6n^2+2=0

We multiply all the terms by the denominator


3n+(-2n)+2*6n^2=0

Wy multiply elements

12n^2+3n+(-2n)=0

We get rid of parentheses

12n^2+3n-2n=0

We add all the numbers together, and all the variables

12n^2+n=0

a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
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*12}=\frac{-2}{24}
=-1/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24}
=0
$