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

Solution for 6/x+2=5/3x+1 equation:

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

We move all terms to the left:

6/x+2-(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

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

We calculate fractions


18x/3x^2+(-5x)/3x^2-1+2=0

We add all the numbers together, and all the variables

18x/3x^2+(-5x)/3x^2+1=0

We multiply all the terms by the denominator


18x+(-5x)+1*3x^2=0

Wy multiply elements

3x^2+18x+(-5x)=0

We get rid of parentheses

3x^2+18x-5x=0

We add all the numbers together, and all the variables

3x^2+13x=0

a = 3; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·3·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*3}=\frac{-26}{6}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*3}=\frac{0}{6}
=0
$