C(x)=5x^2-200x+1000

Solution for C(x)=5x^2-200x+1000 equation:

(C)=5C^2-200C+1000

We move all terms to the left:

(C)-(5C^2-200C+1000)=0

We get rid of parentheses

-5C^2+C+200C-1000=0

We add all the numbers together, and all the variables

-5C^2+201C-1000=0

a = -5; b = 201; c = -1000;
Δ = b2-4ac
Δ = 2012-4·(-5)·(-1000)
Δ = 20401
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{-(201)-\sqrt{20401}}{2*-5}=\frac{-201-\sqrt{20401}}{-10}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(201)+\sqrt{20401}}{2*-5}=\frac{-201+\sqrt{20401}}{-10}
$