4/6n+8=1/2n+2

Solution for 4/6n+8=1/2n+2 equation:

4/6n+8=1/2n+2

We move all terms to the left:

4/6n+8-(1/2n+2)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



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

n∈R


We get rid of parentheses

4/6n-1/2n-2+8=0

We calculate fractions


8n/12n^2+(-6n)/12n^2-2+8=0

We add all the numbers together, and all the variables

8n/12n^2+(-6n)/12n^2+6=0

We multiply all the terms by the denominator


8n+(-6n)+6*12n^2=0

Wy multiply elements

72n^2+8n+(-6n)=0

We get rid of parentheses

72n^2+8n-6n=0

We add all the numbers together, and all the variables

72n^2+2n=0

a = 72; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·72·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*72}=\frac{-4}{144}
=-1/36
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*72}=\frac{0}{144}
=0
$