x+6=1/2x+6

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



x+6=1/2x+6
We move all terms to the left:
x+6-(1/2x+6)=0
Domain of the equation: 2x+6)!=0
x∈R
We get rid of parentheses
x-1/2x-6+6=0
We multiply all the terms by the denominator
x*2x-6*2x+6*2x-1=0
Wy multiply elements
2x^2-12x+12x-1=0
We add all the numbers together, and all the variables
2x^2-1=0
a = 2; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2·(-1)
Δ = 8
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:
$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*2}=\frac{0-2\sqrt{2}}{4} =-\frac{2\sqrt{2}}{4} =-\frac{\sqrt{2}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*2}=\frac{0+2\sqrt{2}}{4} =\frac{2\sqrt{2}}{4} =\frac{\sqrt{2}}{2} $

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