4/9n+7=5/3n-4

Solution for 4/9n+7=5/3n-4 equation:

4/9n+7=5/3n-4

We move all terms to the left:

4/9n+7-(5/3n-4)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



Domain of the equation: 3n-4)!=0

n∈R


We get rid of parentheses

4/9n-5/3n+4+7=0

We calculate fractions


12n/27n^2+(-45n)/27n^2+4+7=0

We add all the numbers together, and all the variables

12n/27n^2+(-45n)/27n^2+11=0

We multiply all the terms by the denominator


12n+(-45n)+11*27n^2=0

Wy multiply elements

297n^2+12n+(-45n)=0

We get rid of parentheses

297n^2+12n-45n=0

We add all the numbers together, and all the variables

297n^2-33n=0

a = 297; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·297·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*297}=\frac{0}{594}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*297}=\frac{66}{594}
=1/9
$