4800=16t^2

Solution for 4800=16t^2 equation:

4800=16t^2

We move all terms to the left:

4800-(16t^2)=0

a = -16; b = 0; c = +4800;
Δ = b2-4ac
Δ = 02-4·(-16)·4800
Δ = 307200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{307200}=\sqrt{102400*3}=\sqrt{102400}*\sqrt{3}=320\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-320\sqrt{3}}{2*-16}=\frac{0-320\sqrt{3}}{-32}
=-\frac{320\sqrt{3}}{-32}
=-\frac{10\sqrt{3}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+320\sqrt{3}}{2*-16}=\frac{0+320\sqrt{3}}{-32}
=\frac{320\sqrt{3}}{-32}
=\frac{10\sqrt{3}}{-1}
$