8=4+24t-16t^2

Solution for 8=4+24t-16t^2 equation:

8=4+24t-16t^2

We move all terms to the left:

8-(4+24t-16t^2)=0

We get rid of parentheses

16t^2-24t-4+8=0

We add all the numbers together, and all the variables

16t^2-24t+4=0

a = 16; b = -24; c = +4;
Δ = b2-4ac
Δ = -242-4·16·4
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{5}}{2*16}=\frac{24-8\sqrt{5}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{5}}{2*16}=\frac{24+8\sqrt{5}}{32}
$