-16t^2+50t+1000=0

Solution for -16t^2+50t+1000=0 equation:

-16t^2+50t+1000=0

a = -16; b = 50; c = +1000;
Δ = b2-4ac
Δ = 502-4·(-16)·1000
Δ = 66500
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:

$\sqrt{\Delta}=\sqrt{66500}=\sqrt{100*665}=\sqrt{100}*\sqrt{665}=10\sqrt{665}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{665}}{2*-16}=\frac{-50-10\sqrt{665}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{665}}{2*-16}=\frac{-50+10\sqrt{665}}{-32}
$