x+2/x-6+9/x+5=17

Solution for x+2/x-6+9/x+5=17 equation:

x+2/x-6+9/x+5=17

We move all terms to the left:

x+2/x-6+9/x+5-(17)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x+9/x-18=0

We multiply all the terms by the denominator


x*x-18*x+2+9=0

We add all the numbers together, and all the variables

-18x+x*x+11=0

Wy multiply elements

x^2-18x+11=0

a = 1; b = -18; c = +11;
Δ = b2-4ac
Δ = -182-4·1·11
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{70}}{2*1}=\frac{18-2\sqrt{70}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{70}}{2*1}=\frac{18+2\sqrt{70}}{2}
$