C(x)=0.2x^2-128x+28.543

Solution for C(x)=0.2x^2-128x+28.543 equation:

(C)=0.2C^2-128C+28.543

We move all terms to the left:

(C)-(0.2C^2-128C+28.543)=0

We get rid of parentheses

-0.2C^2+C+128C-28.543=0

We add all the numbers together, and all the variables

-0.2C^2+129C-28.543=0

a = -0.2; b = 129; c = -28.543;
Δ = b2-4ac
Δ = 1292-4·(-0.2)·(-28.543)
Δ = 16618.1656
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{-(129)-\sqrt{16618.1656}}{2*-0.2}=\frac{-129-\sqrt{16618.1656}}{-0.4}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(129)+\sqrt{16618.1656}}{2*-0.2}=\frac{-129+\sqrt{16618.1656}}{-0.4}
$