C(q)=0,1q2+70q+200

Solution for C(q)=0,1q2+70q+200 equation:

(C)=0.1C^2+70C+200

We move all terms to the left:

(C)-(0.1C^2+70C+200)=0

We get rid of parentheses

-0.1C^2+C-70C-200=0

We add all the numbers together, and all the variables

-0.1C^2-69C-200=0

a = -0.1; b = -69; c = -200;
Δ = b2-4ac
Δ = -692-4·(-0.1)·(-200)
Δ = 4681
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{-(-69)-\sqrt{4681}}{2*-0.1}=\frac{69-\sqrt{4681}}{-0.2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{4681}}{2*-0.1}=\frac{69+\sqrt{4681}}{-0.2}
$