-8x(x+1)=1

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

-8x(x+1)=1

We move all terms to the left:

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

We multiply parentheses

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

a = -8; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·(-8)·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{2}}{2*-8}=\frac{8-4\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{2}}{2*-8}=\frac{8+4\sqrt{2}}{-16}
$