10/3x-1=3/x

Solution for 10/3x-1=3/x equation:

10/3x-1=3/x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


10x/3x^2+(-9x)/3x^2-1=0

We multiply all the terms by the denominator


10x+(-9x)-1*3x^2=0

Wy multiply elements

-3x^2+10x+(-9x)=0

We get rid of parentheses

-3x^2+10x-9x=0

We add all the numbers together, and all the variables

-3x^2+x=0

a = -3; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-3)·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*-3}=\frac{-2}{-6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-3}=\frac{0}{-6}
=0
$