2/3x=4x-2

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

2/3x=4x-2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-4x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+6x+2=0

a = -12; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-12)·2
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*-12}=\frac{-6-2\sqrt{33}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*-12}=\frac{-6+2\sqrt{33}}{-24}
$