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

Solution for 3x-5=(5x-3)/x equation:

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

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


3x*x)-((5x-3)-5*x)=0

Wy multiply elements

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