4-2/9n=5+2/3n

Solution for 4-2/9n=5+2/3n equation:

4-2/9n=5+2/3n

We move all terms to the left:

4-2/9n-(5+2/3n)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-2/9n-(2/3n+5)+4=0

We get rid of parentheses

-2/9n-2/3n-5+4=0

We calculate fractions


(-6n)/27n^2+(-18n)/27n^2-5+4=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^2-24n=0

a = -27; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-27)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-27}=\frac{0}{-54}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-27}=\frac{48}{-54}
=-8/9
$