2/3x=6x

Solution for 2/3x=6x equation:

2/3x=6x

We move all terms to the left:

2/3x-(6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+2/3x=0

We multiply all the terms by the denominator


-6x*3x+2=0

Wy multiply elements

-18x^2+2=0

a = -18; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-18)·2
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-18}=\frac{-12}{-36}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-18}=\frac{12}{-36}
=-1/3
$