C(x)=30x-0.005x^2

Solution for C(x)=30x-0.005x^2 equation:

(C)=30C-0.005C^2

We move all terms to the left:

(C)-(30C-0.005C^2)=0

We get rid of parentheses

0.005C^2-30C+C=0

We add all the numbers together, and all the variables

0.005C^2-29C=0

a = 0.005; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·0.005·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*0.005}=\frac{0}{0.01}
=0
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*0.005}=\frac{58}{0.01}
=5800
$