I(x)=180x-x2

Solution for I(x)=180x-x2 equation:

(I)=180I-I2

We move all terms to the left:

(I)-(180I-I2)=0

We add all the numbers together, and all the variables

-(+180I-1I^2)+I=0

We get rid of parentheses

1I^2-180I+I=0

We add all the numbers together, and all the variables

I^2-179I=0

a = 1; b = -179; c = 0;
Δ = b2-4ac
Δ = -1792-4·1·0
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-179)-179}{2*1}=\frac{0}{2}
=0
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+179}{2*1}=\frac{358}{2}
=179
$