108/3x=2x

Solution for 108/3x=2x equation:

108/3x=2x

We move all terms to the left:

108/3x-(2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+108/3x=0

We multiply all the terms by the denominator


-2x*3x+108=0

Wy multiply elements

-6x^2+108=0

a = -6; b = 0; c = +108;
Δ = b2-4ac
Δ = 02-4·(-6)·108
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*-6}=\frac{0-36\sqrt{2}}{-12}
=-\frac{36\sqrt{2}}{-12}
=-\frac{3\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*-6}=\frac{0+36\sqrt{2}}{-12}
=\frac{36\sqrt{2}}{-12}
=\frac{3\sqrt{2}}{-1}
$