-16t^2+32t+100=0

Solution for -16t^2+32t+100=0 equation:

-16t^2+32t+100=0

a = -16; b = 32; c = +100;
Δ = b2-4ac
Δ = 322-4·(-16)·100
Δ = 7424
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:

$\sqrt{\Delta}=\sqrt{7424}=\sqrt{256*29}=\sqrt{256}*\sqrt{29}=16\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16\sqrt{29}}{2*-16}=\frac{-32-16\sqrt{29}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16\sqrt{29}}{2*-16}=\frac{-32+16\sqrt{29}}{-32}
$