0=16t^2+84t-10

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

0=16t^2+84t-10

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -16; b = -84; c = +10;
Δ = b2-4ac
Δ = -842-4·(-16)·10
Δ = 7696
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:

$\sqrt{\Delta}=\sqrt{7696}=\sqrt{16*481}=\sqrt{16}*\sqrt{481}=4\sqrt{481}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{481}}{2*-16}=\frac{84-4\sqrt{481}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{481}}{2*-16}=\frac{84+4\sqrt{481}}{-32}
$