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

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

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

We move all terms to the left:

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


Domain of the equation: 3)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-12x+4=0

a = 6; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·6·4
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*6}=\frac{12-4\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*6}=\frac{12+4\sqrt{3}}{12}
$