4-(2/3x)=2x

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

4-(2/3x)=2x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·(-6)·(-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{-(12)-4\sqrt{6}}{2*-6}=\frac{-12-4\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*-6}=\frac{-12+4\sqrt{6}}{-12}
$