C(x)=-x^2+40x+5775

Solution for C(x)=-x^2+40x+5775 equation:

(C)=-C^2+40C+5775

We move all terms to the left:

(C)-(-C^2+40C+5775)=0

We get rid of parentheses

C^2-40C+C-5775=0

We add all the numbers together, and all the variables

C^2-39C-5775=0

a = 1; b = -39; c = -5775;
Δ = b2-4ac
Δ = -392-4·1·(-5775)
Δ = 24621
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{-(-39)-\sqrt{24621}}{2*1}=\frac{39-\sqrt{24621}}{2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{24621}}{2*1}=\frac{39+\sqrt{24621}}{2}
$