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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-2)·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-2}=\frac{12}{-4}
=-3
$