2x/3x=4x

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

2x/3x=4x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+2x/3x=0

We multiply all the terms by the denominator


-4x*3x+2x=0

We add all the numbers together, and all the variables

2x-4x*3x=0

Wy multiply elements

-12x^2+2x=0

a = -12; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-12)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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