8^2x=1/16

Solution for 8^2x=1/16 equation:

8^2x=1/16

We move all terms to the left:

8^2x-(1/16)=0

We add all the numbers together, and all the variables

8^2x-(+1/16)=0

We get rid of parentheses

8^2x-1/16=0

We multiply all the terms by the denominator


8^2x*16-1=0

Wy multiply elements

128x^2-1=0

a = 128; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·128·(-1)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*128}=\frac{0-16\sqrt{2}}{256}
=-\frac{16\sqrt{2}}{256}
=-\frac{\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*128}=\frac{0+16\sqrt{2}}{256}
=\frac{16\sqrt{2}}{256}
=\frac{\sqrt{2}}{16}
$