0=8(x^2)+8x-1

Solution for 0=8(x^2)+8x-1 equation:

0=8(x^2)+8x-1

We move all terms to the left:

0-(8(x^2)+8x-1)=0

We add all the numbers together, and all the variables

-(8x^2+8x-1)=0

We get rid of parentheses

-8x^2-8x+1=0

a = -8; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-8)·1
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*-8}=\frac{8-4\sqrt{6}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*-8}=\frac{8+4\sqrt{6}}{-16}
$