1/2x+5=2/x-5

Solution for 1/2x+5=2/x-5 equation:

1/2x+5=2/x-5

We move all terms to the left:

1/2x+5-(2/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

1/2x-2/x+5+5=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


x+(-4x)+10*2x^2=0

Wy multiply elements

20x^2+x+(-4x)=0

We get rid of parentheses

20x^2+x-4x=0

We add all the numbers together, and all the variables

20x^2-3x=0

a = 20; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·20·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*20}=\frac{6}{40}
=3/20
$