2/4x=64x

Solution for 2/4x=64x equation:

2/4x=64x

We move all terms to the left:

2/4x-(64x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-64x+2/4x=0

We multiply all the terms by the denominator


-64x*4x+2=0

Wy multiply elements

-256x^2+2=0

a = -256; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-256)·2
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{-(0)-32\sqrt{2}}{2*-256}=\frac{0-32\sqrt{2}}{-512}
=-\frac{32\sqrt{2}}{-512}
=-\frac{\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{2}}{2*-256}=\frac{0+32\sqrt{2}}{-512}
=\frac{32\sqrt{2}}{-512}
=\frac{\sqrt{2}}{-16}
$