1/3n-21/6n=1/2

Solution for 1/3n-21/6n=1/2 equation:

1/3n-21/6n=1/2

We move all terms to the left:

1/3n-21/6n-(1/2)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

1/3n-21/6n-(+1/2)=0

We get rid of parentheses

1/3n-21/6n-1/2=0

We calculate fractions


(-108n^2)/72n^2+24n/72n^2+(-252n)/72n^2=0

We multiply all the terms by the denominator


(-108n^2)+24n+(-252n)=0

We get rid of parentheses

-108n^2+24n-252n=0

We add all the numbers together, and all the variables

-108n^2-228n=0

a = -108; b = -228; c = 0;
Δ = b2-4ac
Δ = -2282-4·(-108)·0
Δ = 51984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51984}=228$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-228}{2*-108}=\frac{0}{-216}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+228}{2*-108}=\frac{456}{-216}
=-2+1/9
$