10/3x+1=2/x+3

Solution for 10/3x+1=2/x+3 equation:

10/3x+1=2/x+3

We move all terms to the left:

10/3x+1-(2/x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

10/3x-2/x-3+1=0

We calculate fractions


10x/3x^2+(-6x)/3x^2-3+1=0

We add all the numbers together, and all the variables

10x/3x^2+(-6x)/3x^2-2=0

We multiply all the terms by the denominator


10x+(-6x)-2*3x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+4x=0

a = -6; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-6)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-6}=\frac{-8}{-12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-6}=\frac{0}{-12}
=0
$