x=576/x

Solution for x=576/x equation:

x=576/x

We move all terms to the left:

x-(576/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+576/x)=0

We get rid of parentheses

x-576/x=0

We multiply all the terms by the denominator


x*x-576=0

Wy multiply elements

x^2-576=0

a = 1; b = 0; c = -576;
Δ = b2-4ac
Δ = 02-4·1·(-576)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*1}=\frac{48}{2}
=24
$