0=4t^2-8t-1

Solution for 0=4t^2-8t-1 equation:

0=4t^2-8t-1

We move all terms to the left:

0-(4t^2-8t-1)=0

We add all the numbers together, and all the variables

-(4t^2-8t-1)=0

We get rid of parentheses

-4t^2+8t+1=0

a = -4; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-4)·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{5}}{2*-4}=\frac{-8-4\sqrt{5}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{5}}{2*-4}=\frac{-8+4\sqrt{5}}{-8}
$