2/x+(x-2)/4=23/(4x)

Solution for 2/x+(x-2)/4=23/(4x) equation:

2/x+(x-2)/4=23/(4x)

We move all terms to the left:

2/x+(x-2)/4-(23/(4x))=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+(x-2)/4-(+23/4x)=0

We get rid of parentheses

2/x+(x-2)/4-23/4x=0

We calculate fractions


128x/64x^2+(x^2-2x)/64x^2+(-23x)/64x^2=0

We multiply all the terms by the denominator


128x+(x^2-2x)+(-23x)=0

We get rid of parentheses

x^2+128x-2x-23x=0

We add all the numbers together, and all the variables

x^2+103x=0

a = 1; b = 103; c = 0;
Δ = b2-4ac
Δ = 1032-4·1·0
Δ = 10609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10609}=103$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-103}{2*1}=\frac{-206}{2}
=-103
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+103}{2*1}=\frac{0}{2}
=0
$