0=2x-4/3x+1

Solution for 0=2x-4/3x+1 equation:

0=2x-4/3x+1

We move all terms to the left:

0-(2x-4/3x+1)=0


Domain of the equation: 3x+1)!=0

x∈R


We add all the numbers together, and all the variables

-(2x-4/3x+1)=0

We get rid of parentheses

-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}
$