8=-16t^2+40t+4

Solution for 8=-16t^2+40t+4 equation:

8=-16t^2+40t+4

We move all terms to the left:

8-(-16t^2+40t+4)=0

We get rid of parentheses

16t^2-40t-4+8=0

We add all the numbers together, and all the variables

16t^2-40t+4=0

a = 16; b = -40; c = +4;
Δ = b2-4ac
Δ = -402-4·16·4
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{21}}{2*16}=\frac{40-8\sqrt{21}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{21}}{2*16}=\frac{40+8\sqrt{21}}{32}
$