2/3x=x*4

Solution for 2/3x=x*4 equation:

2/3x=x*4

We move all terms to the left:

2/3x-(x*4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(+x*4)=0

We get rid of parentheses

2/3x-x*4=0

We multiply all the terms by the denominator


-(x*4)*3x+2=0

We add all the numbers together, and all the variables

-(+x*4)*3x+2=0

We multiply parentheses

-12x^2+2=0

a = -12; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-12)·2
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-12}=\frac{0-4\sqrt{6}}{-24}
=-\frac{4\sqrt{6}}{-24}
=-\frac{\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-12}=\frac{0+4\sqrt{6}}{-24}
=\frac{4\sqrt{6}}{-24}
=\frac{\sqrt{6}}{-6}
$