n/1.5n+3.75n=500

Solution for n/1.5n+3.75n=500 equation:

n/1.5n+3.75n=500

We move all terms to the left:

n/1.5n+3.75n-(500)=0


Domain of the equation: 1.5n!=0

n!=0/1.5

n!=0

n∈R


We add all the numbers together, and all the variables

3.75n+n/1.5n-500=0

We multiply all the terms by the denominator


(3.75n)*1.5n+n-500*1.5n=0

We add all the numbers together, and all the variables

(+3.75n)*1.5n+n-500*1.5n=0

We add all the numbers together, and all the variables

n+(+3.75n)*1.5n-500*1.5n=0

We multiply parentheses

3n^2+n-500*1.5n=0

Wy multiply elements

3n^2+n-500n=0

We add all the numbers together, and all the variables

3n^2-499n=0

a = 3; b = -499; c = 0;
Δ = b2-4ac
Δ = -4992-4·3·0
Δ = 249001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{249001}=499$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-499)-499}{2*3}=\frac{0}{6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-499)+499}{2*3}=\frac{998}{6}
=166+1/3
$