2/x-3=5/3x+1

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

2/x-3=5/3x+1

We move all terms to the left:

2/x-3-(5/3x+1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


6x/3x^2+(-5x)/3x^2-1-3=0

We add all the numbers together, and all the variables

6x/3x^2+(-5x)/3x^2-4=0

We multiply all the terms by the denominator


6x+(-5x)-4*3x^2=0

Wy multiply elements

-12x^2+6x+(-5x)=0

We get rid of parentheses

-12x^2+6x-5x=0

We add all the numbers together, and all the variables

-12x^2+x=0

a = -12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-12)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-12}=\frac{-2}{-24}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-12}=\frac{0}{-24}
=0
$