0=-16t^2-96t+144

Solution for 0=-16t^2-96t+144 equation:

0=-16t^2-96t+144

We move all terms to the left:

0-(-16t^2-96t+144)=0

We add all the numbers together, and all the variables

-(-16t^2-96t+144)=0

We get rid of parentheses

16t^2+96t-144=0

a = 16; b = 96; c = -144;
Δ = b2-4ac
Δ = 962-4·16·(-144)
Δ = 18432
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:

$\sqrt{\Delta}=\sqrt{18432}=\sqrt{9216*2}=\sqrt{9216}*\sqrt{2}=96\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96\sqrt{2}}{2*16}=\frac{-96-96\sqrt{2}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96\sqrt{2}}{2*16}=\frac{-96+96\sqrt{2}}{32}
$