11=x.X+44/2x

Solution for 11=x.X+44/2x equation:

11=x.x+44/2x

We move all terms to the left:

11-(x.x+44/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x.x+44/2x)+11=0

We get rid of parentheses

-x.x-44/2x+11=0

We multiply all the terms by the denominator


-(x.x)*2x+11*2x-44=0

We add all the numbers together, and all the variables

-(+x.x)*2x+11*2x-44=0

We multiply parentheses

-2x^2+11*2x-44=0

Wy multiply elements

-2x^2+22x-44=0

a = -2; b = 22; c = -44;
Δ = b2-4ac
Δ = 222-4·(-2)·(-44)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{33}}{2*-2}=\frac{-22-2\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{33}}{2*-2}=\frac{-22+2\sqrt{33}}{-4}
$