2x+1/x=-6

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



2x+1/x=-6
We move all terms to the left:
2x+1/x-(-6)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
2x+1/x+6=0
We multiply all the terms by the denominator
2x*x+6*x+1=0
We add all the numbers together, and all the variables
6x+2x*x+1=0
Wy multiply elements
2x^2+6x+1=0
a = 2; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·2·1
Δ = 28
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:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{7}}{2*2}=\frac{-6-2\sqrt{7}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*2}=\frac{-6+2\sqrt{7}}{4} $

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