128=8x^2-2x+1

Solution for 128=8x^2-2x+1 equation:

128=8x^2-2x+1

We move all terms to the left:

128-(8x^2-2x+1)=0

We get rid of parentheses

-8x^2+2x-1+128=0

We add all the numbers together, and all the variables

-8x^2+2x+127=0

a = -8; b = 2; c = +127;
Δ = b2-4ac
Δ = 22-4·(-8)·127
Δ = 4068
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:

$\sqrt{\Delta}=\sqrt{4068}=\sqrt{36*113}=\sqrt{36}*\sqrt{113}=6\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{113}}{2*-8}=\frac{-2-6\sqrt{113}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{113}}{2*-8}=\frac{-2+6\sqrt{113}}{-16}
$