3/n-1/2=6/3n

Solution for 3/n-1/2=6/3n equation:

3/n-1/2=6/3n

We move all terms to the left:

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


Domain of the equation: 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

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

We get rid of parentheses

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

We calculate fractions


(-9n^2)/12n^2+36n/12n^2+(-24n)/12n^2=0

We multiply all the terms by the denominator


(-9n^2)+36n+(-24n)=0

We get rid of parentheses

-9n^2+36n-24n=0

We add all the numbers together, and all the variables

-9n^2+12n=0

a = -9; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-9)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-9}=\frac{-24}{-18}
=1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-9}=\frac{0}{-18}
=0
$