C(x)=x^2-4000+100

Solution for C(x)=x^2-4000+100 equation:

(C)=C^2-4000+100

We move all terms to the left:

(C)-(C^2-4000+100)=0

We get rid of parentheses

-C^2+C+4000-100=0

We add all the numbers together, and all the variables

-1C^2+C+3900=0

a = -1; b = 1; c = +3900;
Δ = b2-4ac
Δ = 12-4·(-1)·3900
Δ = 15601
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{-(1)-\sqrt{15601}}{2*-1}=\frac{-1-\sqrt{15601}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{15601}}{2*-1}=\frac{-1+\sqrt{15601}}{-2}
$