C(x)=3x^2-1200x+130,500

Solution for C(x)=3x^2-1200x+130,500 equation:

(C)=3C^2-1200C+130.500

We move all terms to the left:

(C)-(3C^2-1200C+130.500)=0

We get rid of parentheses

-3C^2+C+1200C-130.500=0

We add all the numbers together, and all the variables

-3C^2+1201C-130.5=0

a = -3; b = 1201; c = -130.5;
Δ = b2-4ac
Δ = 12012-4·(-3)·(-130.5)
Δ = 1440835
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{-(1201)-\sqrt{1440835}}{2*-3}=\frac{-1201-\sqrt{1440835}}{-6}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1201)+\sqrt{1440835}}{2*-3}=\frac{-1201+\sqrt{1440835}}{-6}
$