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

Solution for -40=-16t^2+72t+40 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16t^2-72t-80=0

a = 16; b = -72; c = -80;
Δ = b2-4ac
Δ = -722-4·16·(-80)
Δ = 10304
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:

$\sqrt{\Delta}=\sqrt{10304}=\sqrt{64*161}=\sqrt{64}*\sqrt{161}=8\sqrt{161}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{161}}{2*16}=\frac{72-8\sqrt{161}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{161}}{2*16}=\frac{72+8\sqrt{161}}{32}
$