0=-16t^2+64t+5000

Solution for 0=-16t^2+64t+5000 equation:

0=-16t^2+64t+5000

We move all terms to the left:

0-(-16t^2+64t+5000)=0

We add all the numbers together, and all the variables

-(-16t^2+64t+5000)=0

We get rid of parentheses

16t^2-64t-5000=0

a = 16; b = -64; c = -5000;
Δ = b2-4ac
Δ = -642-4·16·(-5000)
Δ = 324096
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:

$\sqrt{\Delta}=\sqrt{324096}=\sqrt{256*1266}=\sqrt{256}*\sqrt{1266}=16\sqrt{1266}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{1266}}{2*16}=\frac{64-16\sqrt{1266}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{1266}}{2*16}=\frac{64+16\sqrt{1266}}{32}
$