1/3n+1/6n=27

Solution for 1/3n+1/6n=27 equation:

1/3n+1/6n=27

We move all terms to the left:

1/3n+1/6n-(27)=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 calculate fractions


6n/18n^2+3n/18n^2-27=0

We multiply all the terms by the denominator


6n+3n-27*18n^2=0

We add all the numbers together, and all the variables

9n-27*18n^2=0

Wy multiply elements

-486n^2+9n=0

a = -486; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-486)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-486}=\frac{-18}{-972}
=1/54
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-486}=\frac{0}{-972}
=0
$