8^2x-1=1/64

Solution for 8^2x-1=1/64 equation:

8^2x-1=1/64

We move all terms to the left:

8^2x-1-(1/64)=0

We add all the numbers together, and all the variables

8^2x-1-(+1/64)=0

We get rid of parentheses

8^2x-1-1/64=0

We multiply all the terms by the denominator


8^2x*64-1-1*64=0

We add all the numbers together, and all the variables

8^2x*64-65=0

Wy multiply elements

512x^2-65=0

a = 512; b = 0; c = -65;
Δ = b2-4ac
Δ = 02-4·512·(-65)
Δ = 133120
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:

$\sqrt{\Delta}=\sqrt{133120}=\sqrt{1024*130}=\sqrt{1024}*\sqrt{130}=32\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{130}}{2*512}=\frac{0-32\sqrt{130}}{1024}
=-\frac{32\sqrt{130}}{1024}
=-\frac{\sqrt{130}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{130}}{2*512}=\frac{0+32\sqrt{130}}{1024}
=\frac{32\sqrt{130}}{1024}
=\frac{\sqrt{130}}{32}
$