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

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

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

We move all terms to the left:

2/9n+1/2-(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+1/2=0

We calculate fractions


81n^2/108n^2+24n/108n^2+(-72n)/108n^2-2=0

We multiply all the terms by the denominator


81n^2+24n+(-72n)-2*108n^2=0

Wy multiply elements

81n^2-216n^2+24n+(-72n)=0

We get rid of parentheses

81n^2-216n^2+24n-72n=0

We add all the numbers together, and all the variables

-135n^2-48n=0

a = -135; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-135)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-135}=\frac{0}{-270}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-135}=\frac{96}{-270}
=-16/45
$