C(x)=600+90x+x2

Solution for C(x)=600+90x+x2 equation:

(C)=600+90C+C2

We move all terms to the left:

(C)-(600+90C+C2)=0

We add all the numbers together, and all the variables

-(+90C+C^2+600)+C=0

We get rid of parentheses

-C^2-90C+C-600=0

We add all the numbers together, and all the variables

-1C^2-89C-600=0

a = -1; b = -89; c = -600;
Δ = b2-4ac
Δ = -892-4·(-1)·(-600)
Δ = 5521
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{-(-89)-\sqrt{5521}}{2*-1}=\frac{89-\sqrt{5521}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+\sqrt{5521}}{2*-1}=\frac{89+\sqrt{5521}}{-2}
$