2/x-6x=12

Solution for 2/x-6x=12 equation:

2/x-6x=12

We move all terms to the left:

2/x-6x-(12)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+2/x-12=0

We multiply all the terms by the denominator


-6x*x-12*x+2=0

We add all the numbers together, and all the variables

-12x-6x*x+2=0

Wy multiply elements

-6x^2-12x+2=0

a = -6; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-6)·2
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*-6}=\frac{12-8\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*-6}=\frac{12+8\sqrt{3}}{-12}
$