X/2x-3=4/x

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

X/2X-3=4/X

We move all terms to the left:

X/2X-3-(4/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

X/2X-(+4/X)-3=0

We get rid of parentheses

X/2X-4/X-3=0

We calculate fractions


X^2/2X^2+(-8X)/2X^2-3=0

We multiply all the terms by the denominator


X^2+(-8X)-3*2X^2=0

Wy multiply elements

X^2-6X^2+(-8X)=0

We get rid of parentheses

X^2-6X^2-8X=0

We add all the numbers together, and all the variables

-5X^2-8X=0

a = -5; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-5)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-5}=\frac{0}{-10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-5}=\frac{16}{-10}
=-1+3/5
$