1/2n+16=2/3n-4

Solution for 1/2n+16=2/3n-4 equation:

1/2n+16=2/3n-4

We move all terms to the left:

1/2n+16-(2/3n-4)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



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

n∈R


We get rid of parentheses

1/2n-2/3n+4+16=0

We calculate fractions


3n/6n^2+(-4n)/6n^2+4+16=0

We add all the numbers together, and all the variables

3n/6n^2+(-4n)/6n^2+20=0

We multiply all the terms by the denominator


3n+(-4n)+20*6n^2=0

Wy multiply elements

120n^2+3n+(-4n)=0

We get rid of parentheses

120n^2+3n-4n=0

We add all the numbers together, and all the variables

120n^2-1n=0

a = 120; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·120·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*120}=\frac{0}{240}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*120}=\frac{2}{240}
=1/120
$