P(t)=-12t^2+480t+30

Solution for P(t)=-12t^2+480t+30 equation:

(P)=-12P^2+480P+30

We move all terms to the left:

(P)-(-12P^2+480P+30)=0

We get rid of parentheses

12P^2-480P+P-30=0

We add all the numbers together, and all the variables

12P^2-479P-30=0

a = 12; b = -479; c = -30;
Δ = b2-4ac
Δ = -4792-4·12·(-30)
Δ = 230881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-479)-\sqrt{230881}}{2*12}=\frac{479-\sqrt{230881}}{24}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-479)+\sqrt{230881}}{2*12}=\frac{479+\sqrt{230881}}{24}
$