48(t)=-16t^2

Solution for 48(t)=-16t^2 equation:

48(t)=-16t^2

We move all terms to the left:

48(t)-(-16t^2)=0

We get rid of parentheses

16t^2+48t=0

a = 16; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·16·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*16}=\frac{-96}{32}
=-3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*16}=\frac{0}{32}
=0
$