2/9n+3=2/3n+2

Solution for 2/9n+3=2/3n+2 equation:

2/9n+3=2/3n+2

We move all terms to the left:

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


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



Domain of the equation: 3n+2)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

27n^2-12n=0

a = 27; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·27·0
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*27}=\frac{0}{54}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*27}=\frac{24}{54}
=4/9
$