x=2-4/3x+2

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

x=2-4/3x+2

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x+4/3x-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-12x+4=0

a = 3; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·3·4
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*3}=\frac{12-4\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*3}=\frac{12+4\sqrt{6}}{6}
$