C(x)=0.6x^2-276x+41.563

Solution for C(x)=0.6x^2-276x+41.563 equation:

(C)=0.6C^2-276C+41.563

We move all terms to the left:

(C)-(0.6C^2-276C+41.563)=0

We get rid of parentheses

-0.6C^2+C+276C-41.563=0

We add all the numbers together, and all the variables

-0.6C^2+277C-41.563=0

a = -0.6; b = 277; c = -41.563;
Δ = b2-4ac
Δ = 2772-4·(-0.6)·(-41.563)
Δ = 76629.2488
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{-(277)-\sqrt{76629.2488}}{2*-0.6}=\frac{-277-\sqrt{76629.2488}}{-1.2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(277)+\sqrt{76629.2488}}{2*-0.6}=\frac{-277+\sqrt{76629.2488}}{-1.2}
$