4/x-4=2/2x-5

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

4/x-4=2/2x-5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/2x^2+(-2x)/2x^2+5-4=0

We add all the numbers together, and all the variables

8x/2x^2+(-2x)/2x^2+1=0

We multiply all the terms by the denominator


8x+(-2x)+1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+6x=0

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