P(t)=-16t^2+800t-4000

Solution for P(t)=-16t^2+800t-4000 equation:

(P)=-16P^2+800P-4000

We move all terms to the left:

(P)-(-16P^2+800P-4000)=0

We get rid of parentheses

16P^2-800P+P+4000=0

We add all the numbers together, and all the variables

16P^2-799P+4000=0

a = 16; b = -799; c = +4000;
Δ = b2-4ac
Δ = -7992-4·16·4000
Δ = 382401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{382401}=\sqrt{81*4721}=\sqrt{81}*\sqrt{4721}=9\sqrt{4721}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-799)-9\sqrt{4721}}{2*16}=\frac{799-9\sqrt{4721}}{32}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-799)+9\sqrt{4721}}{2*16}=\frac{799+9\sqrt{4721}}{32}
$