C(x)=0.5x^2-280x+52,506

Solution for C(x)=0.5x^2-280x+52,506 equation:

(C)=0.5C^2-280C+52.506

We move all terms to the left:

(C)-(0.5C^2-280C+52.506)=0

We get rid of parentheses

-0.5C^2+C+280C-52.506=0

We add all the numbers together, and all the variables

-0.5C^2+281C-52.506=0

a = -0.5; b = 281; c = -52.506;
Δ = b2-4ac
Δ = 2812-4·(-0.5)·(-52.506)
Δ = 78855.988
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{-(281)-\sqrt{78855.988}}{2*-0.5}=\frac{-281-\sqrt{78855.988}}{-1}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(281)+\sqrt{78855.988}}{2*-0.5}=\frac{-281+\sqrt{78855.988}}{-1}
$