1000=(3n^2)/5n

Solution for 1000=(3n^2)/5n equation:

1000=(3n^2)/5n

We move all terms to the left:

1000-((3n^2)/5n)=0


Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We get rid of parentheses

-3n^2/5n+1000=0

We multiply all the terms by the denominator


-3n^2+1000*5n=0

Wy multiply elements

-3n^2+5000n=0

a = -3; b = 5000; c = 0;
Δ = b2-4ac
Δ = 50002-4·(-3)·0
Δ = 25000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25000000}=5000$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-5000}{2*-3}=\frac{-10000}{-6}
=1666+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+5000}{2*-3}=\frac{0}{-6}
=0
$