-4/9n-8+1/3n=7

Solution for -4/9n-8+1/3n=7 equation:

-4/9n-8+1/3n=7

We move all terms to the left:

-4/9n-8+1/3n-(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 add all the numbers together, and all the variables

-4/9n+1/3n-15=0

We calculate fractions


(-12n)/27n^2+9n/27n^2-15=0

We multiply all the terms by the denominator


(-12n)+9n-15*27n^2=0

We add all the numbers together, and all the variables

9n+(-12n)-15*27n^2=0

Wy multiply elements

-405n^2+9n+(-12n)=0

We get rid of parentheses

-405n^2+9n-12n=0

We add all the numbers together, and all the variables

-405n^2-3n=0

a = -405; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-405)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-405}=\frac{0}{-810}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-405}=\frac{6}{-810}
=-1/135
$