4032=16t^2

Solution for 4032=16t^2 equation:

4032=16t^2

We move all terms to the left:

4032-(16t^2)=0

a = -16; b = 0; c = +4032;
Δ = b2-4ac
Δ = 02-4·(-16)·4032
Δ = 258048
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:

$\sqrt{\Delta}=\sqrt{258048}=\sqrt{36864*7}=\sqrt{36864}*\sqrt{7}=192\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-192\sqrt{7}}{2*-16}=\frac{0-192\sqrt{7}}{-32}
=-\frac{192\sqrt{7}}{-32}
=-\frac{6\sqrt{7}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+192\sqrt{7}}{2*-16}=\frac{0+192\sqrt{7}}{-32}
=\frac{192\sqrt{7}}{-32}
=\frac{6\sqrt{7}}{-1}
$