-8x^2+x+1/32=0

Solution for -8x^2+x+1/32=0 equation:

-8x^2+x+1/32=0

We multiply all the terms by the denominator


-8x^2*32+x*32+1=0

Wy multiply elements

-256x^2+32x+1=0

a = -256; b = 32; c = +1;
Δ = b2-4ac
Δ = 322-4·(-256)·1
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32\sqrt{2}}{2*-256}=\frac{-32-32\sqrt{2}}{-512}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32\sqrt{2}}{2*-256}=\frac{-32+32\sqrt{2}}{-512}
$