x+44/2xx=11

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Solution for x+44/2xx=11 equation:



x+44/2xx=11
We move all terms to the left:
x+44/2xx-(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} $

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