20=16t^2+84t

Solution for 20=16t^2+84t equation:

20=16t^2+84t

We move all terms to the left:

20-(16t^2+84t)=0

We get rid of parentheses

-16t^2-84t+20=0

a = -16; b = -84; c = +20;
Δ = b2-4ac
Δ = -842-4·(-16)·20
Δ = 8336
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:

$\sqrt{\Delta}=\sqrt{8336}=\sqrt{16*521}=\sqrt{16}*\sqrt{521}=4\sqrt{521}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{521}}{2*-16}=\frac{84-4\sqrt{521}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{521}}{2*-16}=\frac{84+4\sqrt{521}}{-32}
$