n/8n=n/40

Solution for n/8n=n/40 equation:

n/8n=n/40

We move all terms to the left:

n/8n-(n/40)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We add all the numbers together, and all the variables

n/8n-(+n/40)=0

We get rid of parentheses

n/8n-n/40=0

We calculate fractions


(-8n^2)/320n+40n/320n=0

We multiply all the terms by the denominator


(-8n^2)+40n=0

We get rid of parentheses

-8n^2+40n=0

a = -8; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-8)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-8}=\frac{-80}{-16}
=+5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-8}=\frac{0}{-16}
=0
$