32*64*x^2-128*x+1=0

Solution for 32*64*x^2-128*x+1=0 equation:

32*64x^2-128x+1=0

We add all the numbers together, and all the variables

-128x+32*64x^2+1=0

Wy multiply elements

2048x^2-128x+1=0

a = 2048; b = -128; c = +1;
Δ = b2-4ac
Δ = -1282-4·2048·1
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-64\sqrt{2}}{2*2048}=\frac{128-64\sqrt{2}}{4096}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+64\sqrt{2}}{2*2048}=\frac{128+64\sqrt{2}}{4096}
$