-1/3n+5+2/9n=3

Solution for -1/3n+5+2/9n=3 equation:

-1/3n+5+2/9n=3

We move all terms to the left:

-1/3n+5+2/9n-(3)=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+2/9n+2=0

We calculate fractions


(-9n)/27n^2+6n/27n^2+2=0

We multiply all the terms by the denominator


(-9n)+6n+2*27n^2=0

We add all the numbers together, and all the variables

6n+(-9n)+2*27n^2=0

Wy multiply elements

54n^2+6n+(-9n)=0

We get rid of parentheses

54n^2+6n-9n=0

We add all the numbers together, and all the variables

54n^2-3n=0

a = 54; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·54·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*54}=\frac{0}{108}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*54}=\frac{6}{108}
=1/18
$