C(x)=48400+500x+x^2

Solution for C(x)=48400+500x+x^2 equation:

(C)=48400+500C+C^2

We move all terms to the left:

(C)-(48400+500C+C^2)=0

We get rid of parentheses

-C^2-500C+C-48400=0

We add all the numbers together, and all the variables

-1C^2-499C-48400=0

a = -1; b = -499; c = -48400;
Δ = b2-4ac
Δ = -4992-4·(-1)·(-48400)
Δ = 55401
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{-(-499)-\sqrt{55401}}{2*-1}=\frac{499-\sqrt{55401}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-499)+\sqrt{55401}}{2*-1}=\frac{499+\sqrt{55401}}{-2}
$