0=8t^2-24t-1

Solution for 0=8t^2-24t-1 equation:

0=8t^2-24t-1

We move all terms to the left:

0-(8t^2-24t-1)=0

We add all the numbers together, and all the variables

-(8t^2-24t-1)=0

We get rid of parentheses

-8t^2+24t+1=0

a = -8; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-8)·1
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{38}}{2*-8}=\frac{-24-4\sqrt{38}}{-16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{38}}{2*-8}=\frac{-24+4\sqrt{38}}{-16}
$