(2/x)+7x=-12

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Solution for (2/x)+7x=-12 equation:



(2/x)+7x=-12
We move all terms to the left:
(2/x)+7x-(-12)=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)+7x-(-12)=0
We add all the numbers together, and all the variables
7x+(+2/x)+12=0
We get rid of parentheses
7x+2/x+12=0
We multiply all the terms by the denominator
7x*x+12*x+2=0
We add all the numbers together, and all the variables
12x+7x*x+2=0
Wy multiply elements
7x^2+12x+2=0
a = 7; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·7·2
Δ = 88
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:
$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{22}}{2*7}=\frac{-12-2\sqrt{22}}{14} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{22}}{2*7}=\frac{-12+2\sqrt{22}}{14} $

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