P(t)=-16t2+48t+110

Solution for P(t)=-16t2+48t+110 equation:

(P)=-16P^2+48P+110

We move all terms to the left:

(P)-(-16P^2+48P+110)=0

We get rid of parentheses

16P^2-48P+P-110=0

We add all the numbers together, and all the variables

16P^2-47P-110=0

a = 16; b = -47; c = -110;
Δ = b2-4ac
Δ = -472-4·16·(-110)
Δ = 9249
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{-(-47)-\sqrt{9249}}{2*16}=\frac{47-\sqrt{9249}}{32}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{9249}}{2*16}=\frac{47+\sqrt{9249}}{32}
$