2(x+4)=6/x

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Solution for 2(x+4)=6/x equation:



2(x+4)=6/x
We move all terms to the left:
2(x+4)-(6/x)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2(x+4)-(+6/x)=0
We multiply parentheses
2x-(+6/x)+8=0
We get rid of parentheses
2x-6/x+8=0
We multiply all the terms by the denominator
2x*x+8*x-6=0
We add all the numbers together, and all the variables
8x+2x*x-6=0
Wy multiply elements
2x^2+8x-6=0
a = 2; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·2·(-6)
Δ = 112
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:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*2}=\frac{-8-4\sqrt{7}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*2}=\frac{-8+4\sqrt{7}}{4} $

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