-2=40t-16t^2

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

-2=40t-16t^2

We move all terms to the left:

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

We get rid of parentheses

16t^2-40t-2=0

a = 16; b = -40; c = -2;
Δ = b2-4ac
Δ = -402-4·16·(-2)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-24\sqrt{3}}{2*16}=\frac{40-24\sqrt{3}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+24\sqrt{3}}{2*16}=\frac{40+24\sqrt{3}}{32}
$