11x/x+5=x+5/x

Solution for 11x/x+5=x+5/x equation:

11x/x+5=x+5/x

We move all terms to the left:

11x/x+5-(x+5/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

11x/x-(+x+5/x)+5=0

We get rid of parentheses

11x/x-x-5/x+5=0

We multiply all the terms by the denominator


11x-x*x+5*x-5=0

We add all the numbers together, and all the variables

16x-x*x-5=0

Wy multiply elements

-1x^2+16x-5=0

a = -1; b = 16; c = -5;
Δ = b2-4ac
Δ = 162-4·(-1)·(-5)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{59}}{2*-1}=\frac{-16-2\sqrt{59}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{59}}{2*-1}=\frac{-16+2\sqrt{59}}{-2}
$