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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


x^2/2x+(-5x-20)/2x-2+2=0

We add all the numbers together, and all the variables

x^2/2x+(-5x-20)/2x=0

We multiply all the terms by the denominator


x^2+(-5x-20)=0

We get rid of parentheses

x^2-5x-20=0

a = 1; b = -5; c = -20;
Δ = b2-4ac
Δ = -52-4·1·(-20)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{105}}{2*1}=\frac{5-\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*1}=\frac{5+\sqrt{105}}{2}
$