18/9-1/2n=1/6n+1

Solution for 18/9-1/2n=1/6n+1 equation:

18/9-1/2n=1/6n+1

We move all terms to the left:

18/9-1/2n-(1/6n+1)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 6n+1)!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-6n)/12n^2+(-2n)/12n^2-1+2=0

We add all the numbers together, and all the variables

(-6n)/12n^2+(-2n)/12n^2+1=0

We multiply all the terms by the denominator


(-6n)+(-2n)+1*12n^2=0

Wy multiply elements

12n^2+(-6n)+(-2n)=0

We get rid of parentheses

12n^2-6n-2n=0

We add all the numbers together, and all the variables

12n^2-8n=0

a = 12; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·12·0
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*12}=\frac{0}{24}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*12}=\frac{16}{24}
=2/3
$