0=-16t^2+72t+144

Solution for 0=-16t^2+72t+144 equation:

0=-16t^2+72t+144

We move all terms to the left:

0-(-16t^2+72t+144)=0

We add all the numbers together, and all the variables

-(-16t^2+72t+144)=0

We get rid of parentheses

16t^2-72t-144=0

a = 16; b = -72; c = -144;
Δ = b2-4ac
Δ = -722-4·16·(-144)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-120}{2*16}=\frac{-48}{32}
=-1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+120}{2*16}=\frac{192}{32}
=6
$