I(x)=20,000x-50x2

Solution for I(x)=20,000x-50x2 equation:

(I)=20.000I-50I^2

We move all terms to the left:

(I)-(20.000I-50I^2)=0

We get rid of parentheses

50I^2-20.000I+I=0

We add all the numbers together, and all the variables

50I^2-19I=0

a = 50; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·50·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*50}=\frac{0}{100}
=0
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*50}=\frac{38}{100}
=19/50
$