C(t)=-5t2+100t-80

Solution for C(t)=-5t2+100t-80 equation:

(C)=-5C^2+100C-80

We move all terms to the left:

(C)-(-5C^2+100C-80)=0

We get rid of parentheses

5C^2-100C+C+80=0

We add all the numbers together, and all the variables

5C^2-99C+80=0

a = 5; b = -99; c = +80;
Δ = b2-4ac
Δ = -992-4·5·80
Δ = 8201
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{-(-99)-\sqrt{8201}}{2*5}=\frac{99-\sqrt{8201}}{10}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{8201}}{2*5}=\frac{99+\sqrt{8201}}{10}
$