1/x=256^x

Solution for 1/x=256^x equation:

1/x=256^x

We move all terms to the left:

1/x-(256^x)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


-256^x*x+1=0

Wy multiply elements

-256x^2+1=0

a = -256; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-256)·1
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*-256}=\frac{-32}{-512}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*-256}=\frac{32}{-512}
=-1/16
$