4x-8/x=2

Solution for 4x-8/x=2 equation:

4x-8/x=2

We move all terms to the left:

4x-8/x-(2)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-2*x-8=0

We add all the numbers together, and all the variables

-2x+4x*x-8=0

Wy multiply elements

4x^2-2x-8=0

a = 4; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·4·(-8)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{33}}{2*4}=\frac{2-2\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{33}}{2*4}=\frac{2+2\sqrt{33}}{8}
$