x=2^16/x

Solution for x=2^16/x equation:

x=2^16/x

We move all terms to the left:

x-(2^16/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

x-2^16/x=0

We multiply all the terms by the denominator


x*x-2^16=0

We add all the numbers together, and all the variables

x*x-65536=0

Wy multiply elements

x^2-65536=0

a = 1; b = 0; c = -65536;
Δ = b2-4ac
Δ = 02-4·1·(-65536)
Δ = 262144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{262144}=512$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-512}{2*1}=\frac{-512}{2}
=-256
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+512}{2*1}=\frac{512}{2}
=256
$