4x=12/9x

Solution for 4x=12/9x equation:

4x=12/9x

We move all terms to the left:

4x-(12/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+12/9x)=0

We get rid of parentheses

4x-12/9x=0

We multiply all the terms by the denominator


4x*9x-12=0

Wy multiply elements

36x^2-12=0

a = 36; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·36·(-12)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*36}=\frac{0-24\sqrt{3}}{72}
=-\frac{24\sqrt{3}}{72}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*36}=\frac{0+24\sqrt{3}}{72}
=\frac{24\sqrt{3}}{72}
=\frac{\sqrt{3}}{3}
$