H=x(500-2x,)

Solution for H=x(500-2x,) equation:

=H(500-2H.)

We move all terms to the left:

-(H(500-2H.))=0

We add all the numbers together, and all the variables

-(H(-2H.+500))=0


We calculate terms in parentheses: -(H(-2H.+500)), so:

H(-2H.+500)

We multiply parentheses

-2H^2+500H

Back to the equation:

-(-2H^2+500H)


We get rid of parentheses

2H^2-500H=0

a = 2; b = -500; c = 0;
Δ = b2-4ac
Δ = -5002-4·2·0
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-500}{2*2}=\frac{0}{4}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+500}{2*2}=\frac{1000}{4}
=250
$