4500/x=x*500

Solution for 4500/x=x*500 equation:

4500/x=x*500

We move all terms to the left:

4500/x-(x*500)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4500/x-(+x*500)=0

We get rid of parentheses

4500/x-x*500=0

We multiply all the terms by the denominator


-(x*500)*x+4500=0

We add all the numbers together, and all the variables

-(+x*500)*x+4500=0

We multiply parentheses

-500x^2+4500=0

a = -500; b = 0; c = +4500;
Δ = b2-4ac
Δ = 02-4·(-500)·4500
Δ = 9000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9000000}=3000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3000}{2*-500}=\frac{-3000}{-1000}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3000}{2*-500}=\frac{3000}{-1000}
=-3
$