-16t^2+64t+800=0

Solution for -16t^2+64t+800=0 equation:

-16t^2+64t+800=0

a = -16; b = 64; c = +800;
Δ = b2-4ac
Δ = 642-4·(-16)·800
Δ = 55296
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:

$\sqrt{\Delta}=\sqrt{55296}=\sqrt{9216*6}=\sqrt{9216}*\sqrt{6}=96\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-96\sqrt{6}}{2*-16}=\frac{-64-96\sqrt{6}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+96\sqrt{6}}{2*-16}=\frac{-64+96\sqrt{6}}{-32}
$