Y=x(500-2x)

Solution for Y=x(500-2x) equation:

=Y(500-2Y)

We move all terms to the left:

-(Y(500-2Y))=0

We add all the numbers together, and all the variables

-(Y(-2Y+500))=0


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

Y(-2Y+500)

We multiply parentheses

-2Y^2+500Y

Back to the equation:

-(-2Y^2+500Y)


We get rid of parentheses

2Y^2-500Y=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:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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