x+x+2/x=20

Solution for x+x+2/x=20 equation:

x+x+2/x=20

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+2/x-20=0

We multiply all the terms by the denominator


2x*x-20*x+2=0

We add all the numbers together, and all the variables

-20x+2x*x+2=0

Wy multiply elements

2x^2-20x+2=0

a = 2; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·2·2
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{6}}{2*2}=\frac{20-8\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{6}}{2*2}=\frac{20+8\sqrt{6}}{4}
$