16x=1/64x=

Solution for 16x=1/64x= equation:

16x=1/64x=

We move all terms to the left:

16x-(1/64x)=0


Domain of the equation: 64x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

16x-(+1/64x)=0

We get rid of parentheses

16x-1/64x=0

We multiply all the terms by the denominator


16x*64x-1=0

Wy multiply elements

1024x^2-1=0

a = 1024; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1024·(-1)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*1024}=\frac{-64}{2048}
=-1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*1024}=\frac{64}{2048}
=1/32
$