4/3n-17-5/9n=11

Solution for 4/3n-17-5/9n=11 equation:

4/3n-17-5/9n=11

We move all terms to the left:

4/3n-17-5/9n-(11)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R


We add all the numbers together, and all the variables

4/3n-5/9n-28=0

We calculate fractions


36n/27n^2+(-15n)/27n^2-28=0

We multiply all the terms by the denominator


36n+(-15n)-28*27n^2=0

Wy multiply elements

-756n^2+36n+(-15n)=0

We get rid of parentheses

-756n^2+36n-15n=0

We add all the numbers together, and all the variables

-756n^2+21n=0

a = -756; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-756)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-756}=\frac{-42}{-1512}
=1/36
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-756}=\frac{0}{-1512}
=0
$