11=x+4/x

Solution for 11=x+4/x equation:

11=x+4/x

We move all terms to the left:

11-(x+4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+4/x)+11=0

We get rid of parentheses

-x-4/x+11=0

We multiply all the terms by the denominator


-x*x+11*x-4=0

We add all the numbers together, and all the variables

11x-x*x-4=0

Wy multiply elements

-1x^2+11x-4=0

a = -1; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·(-1)·(-4)
Δ = 105
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{-(11)-\sqrt{105}}{2*-1}=\frac{-11-\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{105}}{2*-1}=\frac{-11+\sqrt{105}}{-2}
$