x+44/2(x)x=11

Solution for x+44/2(x)x=11 equation:

x+44/2(x)x=11

We move all terms to the left:

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


Domain of the equation: 2xx!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


x*2xx-11*2xx+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}
$