0=-16t^2+24t+120

Solution for 0=-16t^2+24t+120 equation:

0=-16t^2+24t+120

We move all terms to the left:

0-(-16t^2+24t+120)=0

We add all the numbers together, and all the variables

-(-16t^2+24t+120)=0

We get rid of parentheses

16t^2-24t-120=0

a = 16; b = -24; c = -120;
Δ = b2-4ac
Δ = -242-4·16·(-120)
Δ = 8256
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:

$\sqrt{\Delta}=\sqrt{8256}=\sqrt{64*129}=\sqrt{64}*\sqrt{129}=8\sqrt{129}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{129}}{2*16}=\frac{24-8\sqrt{129}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{129}}{2*16}=\frac{24+8\sqrt{129}}{32}
$