C(x)=4,000+.3x^2+50x

Solution for C(x)=4,000+.3x^2+50x equation:

(C)=4.000+.3C^2+50C

We move all terms to the left:

(C)-(4.000+.3C^2+50C)=0

We get rid of parentheses

-.3C^2-50C+C-4.000=0

We add all the numbers together, and all the variables

-0.3C^2-49C-4=0

a = -0.3; b = -49; c = -4;
Δ = b2-4ac
Δ = -492-4·(-0.3)·(-4)
Δ = 2396.2
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{-(-49)-\sqrt{2396.2}}{2*-0.3}=\frac{49-\sqrt{2396.2}}{-0.6}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2396.2}}{2*-0.3}=\frac{49+\sqrt{2396.2}}{-0.6}
$