2/3n-16=5/6n+2

Solution for 2/3n-16=5/6n+2 equation:

2/3n-16=5/6n+2

We move all terms to the left:

2/3n-16-(5/6n+2)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 6n+2)!=0

n∈R


We get rid of parentheses

2/3n-5/6n-2-16=0

We calculate fractions


12n/18n^2+(-15n)/18n^2-2-16=0

We add all the numbers together, and all the variables

12n/18n^2+(-15n)/18n^2-18=0

We multiply all the terms by the denominator


12n+(-15n)-18*18n^2=0

Wy multiply elements

-324n^2+12n+(-15n)=0

We get rid of parentheses

-324n^2+12n-15n=0

We add all the numbers together, and all the variables

-324n^2-3n=0

a = -324; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-324)·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*-324}=\frac{0}{-648}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-324}=\frac{6}{-648}
=-1/108
$