C(x)=x^2-180x+20.000

Solution for C(x)=x^2-180x+20.000 equation:

(C)=C^2-180C+20.000

We move all terms to the left:

(C)-(C^2-180C+20.000)=0

We get rid of parentheses

-C^2+C+180C-20.000=0

We add all the numbers together, and all the variables

-1C^2+181C-20=0

a = -1; b = 181; c = -20;
Δ = b2-4ac
Δ = 1812-4·(-1)·(-20)
Δ = 32681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-\sqrt{32681}}{2*-1}=\frac{-181-\sqrt{32681}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+\sqrt{32681}}{2*-1}=\frac{-181+\sqrt{32681}}{-2}
$