8=-16t^2-8t+20

Solution for 8=-16t^2-8t+20 equation:

8=-16t^2-8t+20

We move all terms to the left:

8-(-16t^2-8t+20)=0

We get rid of parentheses

16t^2+8t-20+8=0

We add all the numbers together, and all the variables

16t^2+8t-12=0

a = 16; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·16·(-12)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{13}}{2*16}=\frac{-8-8\sqrt{13}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{13}}{2*16}=\frac{-8+8\sqrt{13}}{32}
$