I=x(1000-50x)

Solution for I=x(1000-50x) equation:

=I(1000-50I)

We move all terms to the left:

-(I(1000-50I))=0

We add all the numbers together, and all the variables

-(I(-50I+1000))=0


We calculate terms in parentheses: -(I(-50I+1000)), so:

I(-50I+1000)

We multiply parentheses

-50I^2+1000I

Back to the equation:

-(-50I^2+1000I)


We get rid of parentheses

50I^2-1000I=0

a = 50; b = -1000; c = 0;
Δ = b2-4ac
Δ = -10002-4·50·0
Δ = 1000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1000000}=1000$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-1000}{2*50}=\frac{0}{100}
=0
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+1000}{2*50}=\frac{2000}{100}
=20
$