6/x-4=8x

Solution for 6/x-4=8x equation:

6/x-4=8x

We move all terms to the left:

6/x-4-(8x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-8x+6/x-4=0

We multiply all the terms by the denominator


-8x*x-4*x+6=0

We add all the numbers together, and all the variables

-4x-8x*x+6=0

Wy multiply elements

-8x^2-4x+6=0

a = -8; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-8)·6
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{13}}{2*-8}=\frac{4-4\sqrt{13}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{13}}{2*-8}=\frac{4+4\sqrt{13}}{-16}
$