X/8^2x-1=1/2

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

X/8^2X-1=1/2

We move all terms to the left:

X/8^2X-1-(1/2)=0


Domain of the equation: 8^2X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X/8^2X-1-(+1/2)=0

We get rid of parentheses

X/8^2X-1-1/2=0

We calculate fractions


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

We multiply all the terms by the denominator


(-8X^2)+2X-1*16X^2=0

Wy multiply elements

(-8X^2)-16X^2+2X=0

We get rid of parentheses

-8X^2-16X^2+2X=0

We add all the numbers together, and all the variables

-24X^2+2X=0

a = -24; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-24)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-24}=\frac{-4}{-48}
=1/12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-24}=\frac{0}{-48}
=0
$