2/x-4=6x

Solution for 2/x-4=6x equation:

2/x-4=6x

We move all terms to the left:

2/x-4-(6x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+2/x-4=0

We multiply all the terms by the denominator


-6x*x-4*x+2=0

We add all the numbers together, and all the variables

-4x-6x*x+2=0

Wy multiply elements

-6x^2-4x+2=0

a = -6; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-6)·2
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-6}=\frac{-4}{-12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-6}=\frac{12}{-12}
=-1
$