2/3x-2=4,x=

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

2/3x-2=4.x=

We move all terms to the left:

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

We get rid of parentheses

2/3x-4.x-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

-12x^2-2*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}
$