10/2x-4=4/x-5

Solution for 10/2x-4=4/x-5 equation:

10/2x-4=4/x-5

We move all terms to the left:

10/2x-4-(4/x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

10/2x-4/x+5-4=0

We calculate fractions


10x/2x^2+(-8x)/2x^2+5-4=0

We add all the numbers together, and all the variables

10x/2x^2+(-8x)/2x^2+1=0

We multiply all the terms by the denominator


10x+(-8x)+1*2x^2=0

Wy multiply elements

2x^2+10x+(-8x)=0

We get rid of parentheses

2x^2+10x-8x=0

We add all the numbers together, and all the variables

2x^2+2x=0

a = 2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·2·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*2}=\frac{0}{4}
=0
$