5/x=10/3x-1

Solution for 5/x=10/3x-1 equation:

5/x=10/3x-1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


15x/3x^2+(-10x)/3x^2+1=0

We multiply all the terms by the denominator


15x+(-10x)+1*3x^2=0

Wy multiply elements

3x^2+15x+(-10x)=0

We get rid of parentheses

3x^2+15x-10x=0

We add all the numbers together, and all the variables

3x^2+5x=0

a = 3; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·3·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*3}=\frac{-10}{6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*3}=\frac{0}{6}
=0
$