4/3x-2=6/2x-1

Solution for 4/3x-2=6/2x-1 equation:

4/3x-2=6/2x-1

We move all terms to the left:

4/3x-2-(6/2x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

4/3x-6/2x+1-2=0

We calculate fractions


8x/6x^2+(-18x)/6x^2+1-2=0

We add all the numbers together, and all the variables

8x/6x^2+(-18x)/6x^2-1=0

We multiply all the terms by the denominator


8x+(-18x)-1*6x^2=0

Wy multiply elements

-6x^2+8x+(-18x)=0

We get rid of parentheses

-6x^2+8x-18x=0

We add all the numbers together, and all the variables

-6x^2-10x=0

a = -6; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-6)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-6}=\frac{20}{-12}
=-1+2/3
$