1224=16t^2

Solution for 1224=16t^2 equation:

1224=16t^2

We move all terms to the left:

1224-(16t^2)=0

a = -16; b = 0; c = +1224;
Δ = b2-4ac
Δ = 02-4·(-16)·1224
Δ = 78336
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:

$\sqrt{\Delta}=\sqrt{78336}=\sqrt{2304*34}=\sqrt{2304}*\sqrt{34}=48\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{34}}{2*-16}=\frac{0-48\sqrt{34}}{-32}
=-\frac{48\sqrt{34}}{-32}
=-\frac{3\sqrt{34}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{34}}{2*-16}=\frac{0+48\sqrt{34}}{-32}
=\frac{48\sqrt{34}}{-32}
=\frac{3\sqrt{34}}{-2}
$