x+x+5/x=17

Solution for x+x+5/x=17 equation:

x+x+5/x=17

We move all terms to the left:

x+x+5/x-(17)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+5/x-17=0

We multiply all the terms by the denominator


2x*x-17*x+5=0

We add all the numbers together, and all the variables

-17x+2x*x+5=0

Wy multiply elements

2x^2-17x+5=0

a = 2; b = -17; c = +5;
Δ = b2-4ac
Δ = -172-4·2·5
Δ = 249
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{-(-17)-\sqrt{249}}{2*2}=\frac{17-\sqrt{249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{249}}{2*2}=\frac{17+\sqrt{249}}{4}
$