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}
$