5x/3x-1=x

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

5x/3x-1=x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-1x*3x+5x-1*3x=0

We add all the numbers together, and all the variables

5x-1x*3x-1*3x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-3x^2+2x=0

a = -3; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-3)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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