30=-16t^2+80t+8

Solution for 30=-16t^2+80t+8 equation:

30=-16t^2+80t+8

We move all terms to the left:

30-(-16t^2+80t+8)=0

We get rid of parentheses

16t^2-80t-8+30=0

We add all the numbers together, and all the variables

16t^2-80t+22=0

a = 16; b = -80; c = +22;
Δ = b2-4ac
Δ = -802-4·16·22
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{78}}{2*16}=\frac{80-8\sqrt{78}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{78}}{2*16}=\frac{80+8\sqrt{78}}{32}
$