9x=9/3x

Solution for 9x=9/3x equation:

9x=9/3x

We move all terms to the left:

9x-(9/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+9/3x)=0

We get rid of parentheses

9x-9/3x=0

We multiply all the terms by the denominator


9x*3x-9=0

Wy multiply elements

27x^2-9=0

a = 27; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·27·(-9)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*27}=\frac{0-18\sqrt{3}}{54}
=-\frac{18\sqrt{3}}{54}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*27}=\frac{0+18\sqrt{3}}{54}
=\frac{18\sqrt{3}}{54}
=\frac{\sqrt{3}}{3}
$