I(x)=80x-0.1x2

Solution for I(x)=80x-0.1x2 equation:

(I)=80I-0.1I^2

We move all terms to the left:

(I)-(80I-0.1I^2)=0

We get rid of parentheses

0.1I^2-80I+I=0

We add all the numbers together, and all the variables

0.1I^2-79I=0

a = 0.1; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·0.1·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*0.1}=\frac{0}{0.2}
=0
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*0.1}=\frac{158}{0.2}
=790
$