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^2-3=0

We multiply all the terms by the denominator


8x+(-18x)-3*6x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-18x^2-10x=0

a = -18; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-18)·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*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-18}=\frac{20}{-36}
=-5/9
$