1/3n-1/9n=-1

Solution for 1/3n-1/9n=-1 equation:

1/3n-1/9n=-1

We move all terms to the left:

1/3n-1/9n-(-1)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R


We add all the numbers together, and all the variables

1/3n-1/9n+1=0

We calculate fractions


9n/27n^2+(-3n)/27n^2+1=0

We multiply all the terms by the denominator


9n+(-3n)+1*27n^2=0

Wy multiply elements

27n^2+9n+(-3n)=0

We get rid of parentheses

27n^2+9n-3n=0

We add all the numbers together, and all the variables

27n^2+6n=0

a = 27; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·27·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*27}=\frac{-12}{54}
=-2/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*27}=\frac{0}{54}
=0
$