x+2/x+15=11/x

Solution for x+2/x+15=11/x equation:

x+2/x+15=11/x

We move all terms to the left:

x+2/x+15-(11/x)=0


Domain of the equation: x!=0

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

x+2/x-(+11/x)+15=0

We get rid of parentheses

x+2/x-11/x+15=0

We multiply all the terms by the denominator


x*x+15*x+2-11=0

We add all the numbers together, and all the variables

15x+x*x-9=0

Wy multiply elements

x^2+15x-9=0

a = 1; b = 15; c = -9;
Δ = b2-4ac
Δ = 152-4·1·(-9)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{29}}{2*1}=\frac{-15-3\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{29}}{2*1}=\frac{-15+3\sqrt{29}}{2}
$