C(t)=-0.45t^2+12t+450

Solution for C(t)=-0.45t^2+12t+450 equation:

(C)=-0.45C^2+12C+450

We move all terms to the left:

(C)-(-0.45C^2+12C+450)=0

We get rid of parentheses

0.45C^2-12C+C-450=0

We add all the numbers together, and all the variables

0.45C^2-11C-450=0

a = 0.45; b = -11; c = -450;
Δ = b2-4ac
Δ = -112-4·0.45·(-450)
Δ = 931
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{931}=\sqrt{49*19}=\sqrt{49}*\sqrt{19}=7\sqrt{19}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7\sqrt{19}}{2*0.45}=\frac{11-7\sqrt{19}}{0.9}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7\sqrt{19}}{2*0.45}=\frac{11+7\sqrt{19}}{0.9}
$