F(t)=-16t^2+384

Solution for F(t)=-16t^2+384 equation:

(F)=-16F^2+384

We move all terms to the left:

(F)-(-16F^2+384)=0

We get rid of parentheses

16F^2+F-384=0

a = 16; b = 1; c = -384;
Δ = b2-4ac
Δ = 12-4·16·(-384)
Δ = 24577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{24577}}{2*16}=\frac{-1-\sqrt{24577}}{32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{24577}}{2*16}=\frac{-1+\sqrt{24577}}{32}
$