-16t^2+15.5+4.25=0

Solution for -16t^2+15.5+4.25=0 equation:

-16t^2+15.5+4.25=0

We add all the numbers together, and all the variables

-16t^2+19.75=0

a = -16; b = 0; c = +19.75;
Δ = b2-4ac
Δ = 02-4·(-16)·19.75
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{79}}{2*-16}=\frac{0-4\sqrt{79}}{-32}
=-\frac{4\sqrt{79}}{-32}
=-\frac{\sqrt{79}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{79}}{2*-16}=\frac{0+4\sqrt{79}}{-32}
=\frac{4\sqrt{79}}{-32}
=\frac{\sqrt{79}}{-8}
$