4/2x-3=5/x

Solution for 4/2x-3=5/x equation:

4/2x-3=5/x

We move all terms to the left:

4/2x-3-(5/x)=0


Domain of the equation: 2x!=0

x!=0/2

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

4/2x-(+5/x)-3=0

We get rid of parentheses

4/2x-5/x-3=0

We calculate fractions


4x/2x^2+(-10x)/2x^2-3=0

We multiply all the terms by the denominator


4x+(-10x)-3*2x^2=0

Wy multiply elements

-6x^2+4x+(-10x)=0

We get rid of parentheses

-6x^2+4x-10x=0

We add all the numbers together, and all the variables

-6x^2-6x=0

a = -6; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-6)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-6}=\frac{12}{-12}
=-1
$