C(x)=3x^2-600x+42,500

Solution for C(x)=3x^2-600x+42,500 equation:

(C)=3C^2-600C+42.500

We move all terms to the left:

(C)-(3C^2-600C+42.500)=0

We get rid of parentheses

-3C^2+C+600C-42.500=0

We add all the numbers together, and all the variables

-3C^2+601C-42.5=0

a = -3; b = 601; c = -42.5;
Δ = b2-4ac
Δ = 6012-4·(-3)·(-42.5)
Δ = 360691
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{-(601)-\sqrt{360691}}{2*-3}=\frac{-601-\sqrt{360691}}{-6}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(601)+\sqrt{360691}}{2*-3}=\frac{-601+\sqrt{360691}}{-6}
$