2/3n-1=2/9n-4

Solution for 2/3n-1=2/9n-4 equation:

2/3n-1=2/9n-4

We move all terms to the left:

2/3n-1-(2/9n-4)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 9n-4)!=0

n∈R


We get rid of parentheses

2/3n-2/9n+4-1=0

We calculate fractions


18n/27n^2+(-6n)/27n^2+4-1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

81n^2+18n+(-6n)=0

We get rid of parentheses

81n^2+18n-6n=0

We add all the numbers together, and all the variables

81n^2+12n=0

a = 81; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·81·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*81}=\frac{-24}{162}
=-4/27
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*81}=\frac{0}{162}
=0
$