(2/x)+7x=-12

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}
$