500=9.81t^2

Solution for 500=9.81t^2 equation:

500=9.81t^2

We move all terms to the left:

500-(9.81t^2)=0

We get rid of parentheses

-9.81t^2+500=0

a = -9.81; b = 0; c = +500;
Δ = b2-4ac
Δ = 02-4·(-9.81)·500
Δ = 19620
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:

$\sqrt{\Delta}=\sqrt{19620}=\sqrt{36*545}=\sqrt{36}*\sqrt{545}=6\sqrt{545}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{545}}{2*-9.81}=\frac{0-6\sqrt{545}}{-19.62}
=-\frac{6\sqrt{545}}{-19.62}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{545}}{2*-9.81}=\frac{0+6\sqrt{545}}{-19.62}
=\frac{6\sqrt{545}}{-19.62}
$