0=-16t^2-10t+84

Solution for 0=-16t^2-10t+84 equation:

0=-16t^2-10t+84

We move all terms to the left:

0-(-16t^2-10t+84)=0

We add all the numbers together, and all the variables

-(-16t^2-10t+84)=0

We get rid of parentheses

16t^2+10t-84=0

a = 16; b = 10; c = -84;
Δ = b2-4ac
Δ = 102-4·16·(-84)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-74}{2*16}=\frac{-84}{32}
=-2+5/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+74}{2*16}=\frac{64}{32}
=2
$