C(x)=2x^2-200x+18,000

Solution for C(x)=2x^2-200x+18,000 equation:

(C)=2C^2-200C+18.000

We move all terms to the left:

(C)-(2C^2-200C+18.000)=0

We get rid of parentheses

-2C^2+C+200C-18.000=0

We add all the numbers together, and all the variables

-2C^2+201C-18=0

a = -2; b = 201; c = -18;
Δ = b2-4ac
Δ = 2012-4·(-2)·(-18)
Δ = 40257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40257}=\sqrt{81*497}=\sqrt{81}*\sqrt{497}=9\sqrt{497}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(201)-9\sqrt{497}}{2*-2}=\frac{-201-9\sqrt{497}}{-4}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(201)+9\sqrt{497}}{2*-2}=\frac{-201+9\sqrt{497}}{-4}
$