2/2x-4=4/x-13

Solution for 2/2x-4=4/x-13 equation:

2/2x-4=4/x-13

We move all terms to the left:

2/2x-4-(4/x-13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-13)!=0

x∈R


We get rid of parentheses

2/2x-4/x+13-4=0

We calculate fractions


2x/2x^2+(-8x)/2x^2+13-4=0

We add all the numbers together, and all the variables

2x/2x^2+(-8x)/2x^2+9=0

We multiply all the terms by the denominator


2x+(-8x)+9*2x^2=0

Wy multiply elements

18x^2+2x+(-8x)=0

We get rid of parentheses

18x^2+2x-8x=0

We add all the numbers together, and all the variables

18x^2-6x=0

a = 18; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·18·0
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*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*18}=\frac{12}{36}
=1/3
$