32/3x=x

Solution for 32/3x=x equation:

32/3x=x

We move all terms to the left:

32/3x-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+32/3x=0

We multiply all the terms by the denominator


-1x*3x+32=0

Wy multiply elements

-3x^2+32=0

a = -3; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-3)·32
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*-3}=\frac{0-8\sqrt{6}}{-6}
=-\frac{8\sqrt{6}}{-6}
=-\frac{4\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*-3}=\frac{0+8\sqrt{6}}{-6}
=\frac{8\sqrt{6}}{-6}
=\frac{4\sqrt{6}}{-3}
$