C(x)=-3(x+10)(x-50)

Solution for C(x)=-3(x+10)(x-50) equation:

(C)=-3(C+10)(C-50)

We move all terms to the left:

(C)-(-3(C+10)(C-50))=0

We multiply parentheses ..

-(-3(+C^2-50C+10C-500))+C=0


We calculate terms in parentheses: -(-3(+C^2-50C+10C-500)), so:

-3(+C^2-50C+10C-500)

We multiply parentheses

-3C^2+150C-30C+1500

We add all the numbers together, and all the variables

-3C^2+120C+1500

Back to the equation:

-(-3C^2+120C+1500)


We get rid of parentheses

3C^2-120C+C-1500=0

We add all the numbers together, and all the variables

3C^2-119C-1500=0

a = 3; b = -119; c = -1500;
Δ = b2-4ac
Δ = -1192-4·3·(-1500)
Δ = 32161
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{-(-119)-\sqrt{32161}}{2*3}=\frac{119-\sqrt{32161}}{6}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{32161}}{2*3}=\frac{119+\sqrt{32161}}{6}
$