I(x)=20000x-50x2

Solution for I(x)=20000x-50x2 equation:

(I)=20000I-50I^2

We move all terms to the left:

(I)-(20000I-50I^2)=0

We get rid of parentheses

50I^2-20000I+I=0

We add all the numbers together, and all the variables

50I^2-19999I=0

a = 50; b = -19999; c = 0;
Δ = b2-4ac
Δ = -199992-4·50·0
Δ = 399960001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{399960001}=19999$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19999)-19999}{2*50}=\frac{0}{100}
=0
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19999)+19999}{2*50}=\frac{39998}{100}
=399+49/50
$