0=8t+-16t2+1

Solution for 0=8t+-16t2+1 equation:

0=8t+-16t^2+1

We move all terms to the left:

0-(8t+-16t^2+1)=0

We add all the numbers together, and all the variables

-(8t+-16t^2+1)=0

We use the square of the difference formula

-(8t-16t^2+1)=0

We get rid of parentheses

16t^2-8t-1=0

a = 16; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·16·(-1)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{2}}{2*16}=\frac{8-8\sqrt{2}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{2}}{2*16}=\frac{8+8\sqrt{2}}{32}
$