20/3n-8=4n/n+2

Solution for 20/3n-8=4n/n+2 equation:

20/3n-8=4n/n+2

We move all terms to the left:

20/3n-8-(4n/n+2)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



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

n∈R


We get rid of parentheses

20/3n-4n/n-2-8=0

We calculate fractions


(-12n^2)/3n^2+20n/3n^2-2-8=0

We add all the numbers together, and all the variables

(-12n^2)/3n^2+20n/3n^2-10=0

We multiply all the terms by the denominator


(-12n^2)+20n-10*3n^2=0

Wy multiply elements

(-12n^2)-30n^2+20n=0

We get rid of parentheses

-12n^2-30n^2+20n=0

We add all the numbers together, and all the variables

-42n^2+20n=0

a = -42; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-42)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-42}=\frac{-40}{-84}
=10/21
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-42}=\frac{0}{-84}
=0
$