2x-4/3x+2=3

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

2x-4/3x+2=3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x-4/3x-1=0

We multiply all the terms by the denominator


2x*3x-1*3x-4=0

Wy multiply elements

6x^2-3x-4=0

a = 6; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·6·(-4)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{105}}{2*6}=\frac{3-\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*6}=\frac{3+\sqrt{105}}{12}
$