(8/x)6x=2

Solution for (8/x)6x=2 equation:

(8/x)6x=2

We move all terms to the left:

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


Domain of the equation: x)6x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/x)6x-2=0

We multiply parentheses

48x^2-2=0

a = 48; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·48·(-2)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*48}=\frac{0-8\sqrt{6}}{96}
=-\frac{8\sqrt{6}}{96}
=-\frac{\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*48}=\frac{0+8\sqrt{6}}{96}
=\frac{8\sqrt{6}}{96}
=\frac{\sqrt{6}}{12}
$