C(x)=400x-0.2x(2)

Solution for C(x)=400x-0.2x(2) equation:

(C)=400C-0.2C(2)

We move all terms to the left:

(C)-(400C-0.2C(2))=0

We add all the numbers together, and all the variables

-(+400C-0.2C^2)+C=0

We get rid of parentheses

0.2C^2-400C+C=0

We add all the numbers together, and all the variables

0.2C^2-399C=0

a = 0.2; b = -399; c = 0;
Δ = b2-4ac
Δ = -3992-4·0.2·0
Δ = 159201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{159201}=399$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-399)-399}{2*0.2}=\frac{0}{0.4}
=0
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-399)+399}{2*0.2}=\frac{798}{0.4}
=1995
$