4/9n-81/3n=7

Solution for 4/9n-81/3n=7 equation:

4/9n-81/3n=7

We move all terms to the left:

4/9n-81/3n-(7)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We calculate fractions


12n/27n^2+(-729n)/27n^2-7=0

We multiply all the terms by the denominator


12n+(-729n)-7*27n^2=0

Wy multiply elements

-189n^2+12n+(-729n)=0

We get rid of parentheses

-189n^2+12n-729n=0

We add all the numbers together, and all the variables

-189n^2-717n=0

a = -189; b = -717; c = 0;
Δ = b2-4ac
Δ = -7172-4·(-189)·0
Δ = 514089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{514089}=717$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-717)-717}{2*-189}=\frac{0}{-378}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-717)+717}{2*-189}=\frac{1434}{-378}
=-3+50/63
$