P(t)=4t^2-16t

Solution for P(t)=4t^2-16t equation:

(P)=4P^2-16P

We move all terms to the left:

(P)-(4P^2-16P)=0

We get rid of parentheses

-4P^2+P+16P=0

We add all the numbers together, and all the variables

-4P^2+17P=0

a = -4; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-4)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-4}=\frac{-34}{-8}
=4+1/4
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-4}=\frac{0}{-8}
=0
$