800/(x+2)+20=800/x

Solution for 800/(x+2)+20=800/x equation:

800/(x+2)+20=800/x

We move all terms to the left:

800/(x+2)+20-(800/x)=0


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

We move all terms containing x to the left, all other terms to the right

x!=-2

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

800/(x+2)-(+800/x)+20=0

We get rid of parentheses

800/(x+2)-800/x+20=0

We calculate fractions


800x/(x^2+2x)+(-800x-1600)/(x^2+2x)+20=0

We multiply all the terms by the denominator


800x+(-800x-1600)+20*(x^2+2x)=0

We multiply parentheses

20x^2+800x+(-800x-1600)+40x=0

We get rid of parentheses

20x^2+800x-800x+40x-1600=0

We add all the numbers together, and all the variables

20x^2+40x-1600=0

a = 20; b = 40; c = -1600;
Δ = b2-4ac
Δ = 402-4·20·(-1600)
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-360}{2*20}=\frac{-400}{40}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+360}{2*20}=\frac{320}{40}
=8
$