0=-16t^2+72t+24

Solution for 0=-16t^2+72t+24 equation:

0=-16t^2+72t+24

We move all terms to the left:

0-(-16t^2+72t+24)=0

We add all the numbers together, and all the variables

-(-16t^2+72t+24)=0

We get rid of parentheses

16t^2-72t-24=0

a = 16; b = -72; c = -24;
Δ = b2-4ac
Δ = -722-4·16·(-24)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{105}}{2*16}=\frac{72-8\sqrt{105}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{105}}{2*16}=\frac{72+8\sqrt{105}}{32}
$