8^2x-4=1/4

Solution for 8^2x-4=1/4 equation:

8^2x-4=1/4

We move all terms to the left:

8^2x-4-(1/4)=0

We add all the numbers together, and all the variables

8^2x-4-(+1/4)=0

We get rid of parentheses

8^2x-4-1/4=0

We multiply all the terms by the denominator


8^2x*4-1-4*4=0

We add all the numbers together, and all the variables

8^2x*4-17=0

Wy multiply elements

32x^2-17=0

a = 32; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·32·(-17)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{34}}{2*32}=\frac{0-8\sqrt{34}}{64}
=-\frac{8\sqrt{34}}{64}
=-\frac{\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{34}}{2*32}=\frac{0+8\sqrt{34}}{64}
=\frac{8\sqrt{34}}{64}
=\frac{\sqrt{34}}{8}
$