80(t)=-16t2-40t+72

Solution for 80(t)=-16t2-40t+72 equation:

80(t)=-16t^2-40t+72

We move all terms to the left:

80(t)-(-16t^2-40t+72)=0

We get rid of parentheses

16t^2+40t+80t-72=0

We add all the numbers together, and all the variables

16t^2+120t-72=0

a = 16; b = 120; c = -72;
Δ = b2-4ac
Δ = 1202-4·16·(-72)
Δ = 19008
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:

$\sqrt{\Delta}=\sqrt{19008}=\sqrt{576*33}=\sqrt{576}*\sqrt{33}=24\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{33}}{2*16}=\frac{-120-24\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{33}}{2*16}=\frac{-120+24\sqrt{33}}{32}
$