0=-16t^2+84

Solution for 0=-16t^2+84 equation:

0=-16t^2+84

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

16t^2-84=0

a = 16; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·16·(-84)
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{21}}{2*16}=\frac{0-16\sqrt{21}}{32}
=-\frac{16\sqrt{21}}{32}
=-\frac{\sqrt{21}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{21}}{2*16}=\frac{0+16\sqrt{21}}{32}
=\frac{16\sqrt{21}}{32}
=\frac{\sqrt{21}}{2}
$