2x-6=x-1/2x

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Solution for 2x-6=x-1/2x equation:



2x-6=x-1/2x
We move all terms to the left:
2x-6-(x-1/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2x-(+x-1/2x)-6=0
We get rid of parentheses
2x-x+1/2x-6=0
We multiply all the terms by the denominator
2x*2x-x*2x-6*2x+1=0
Wy multiply elements
4x^2-2x^2-12x+1=0
We add all the numbers together, and all the variables
2x^2-12x+1=0
a = 2; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·2·1
Δ = 136
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:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{34}}{2*2}=\frac{12-2\sqrt{34}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*2}=\frac{12+2\sqrt{34}}{4} $

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