2x-4=4/3x+2

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

2x-4=4/3x+2

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-6x-12x-4=0

We add all the numbers together, and all the variables

6x^2-18x-4=0

a = 6; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·6·(-4)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*6}=\frac{18-2\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*6}=\frac{18+2\sqrt{105}}{12}
$