T=-16t^2+500

Solution for T=-16t^2+500 equation:

=-16T^2+500

We move all terms to the left:

-(-16T^2+500)=0

We get rid of parentheses

16T^2-500=0

a = 16; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·16·(-500)
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{5}}{2*16}=\frac{0-80\sqrt{5}}{32}
=-\frac{80\sqrt{5}}{32}
=-\frac{5\sqrt{5}}{2}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{5}}{2*16}=\frac{0+80\sqrt{5}}{32}
=\frac{80\sqrt{5}}{32}
=\frac{5\sqrt{5}}{2}
$