5/3x=4/2x+1

Solution for 5/3x=4/2x+1 equation:

5/3x=4/2x+1

We move all terms to the left:

5/3x-(4/2x+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

5/3x-4/2x-1=0

We calculate fractions


10x/6x^2+(-12x)/6x^2-1=0

We multiply all the terms by the denominator


10x+(-12x)-1*6x^2=0

Wy multiply elements

-6x^2+10x+(-12x)=0

We get rid of parentheses

-6x^2+10x-12x=0

We add all the numbers together, and all the variables

-6x^2-2x=0

a = -6; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-6)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-6}=\frac{4}{-12}
=-1/3
$