1/6n+2/3n=1

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

1/6n+2/3n=1

We move all terms to the left:

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


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We calculate fractions


3n/18n^2+12n/18n^2-1=0

We multiply all the terms by the denominator


3n+12n-1*18n^2=0

We add all the numbers together, and all the variables

15n-1*18n^2=0

Wy multiply elements

-18n^2+15n=0

a = -18; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-18)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-18}=\frac{-30}{-36}
=5/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-18}=\frac{0}{-36}
=0
$