4x-8/x=2x-2/2

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

4x-8/x=2x-2/2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x-8/x-(2x-1)=0

We get rid of parentheses

4x-8/x-2x+1=0

We multiply all the terms by the denominator


4x*x-2x*x+1*x-8=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

2x^2+x-8=0

a = 2; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·2·(-8)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{65}}{2*2}=\frac{-1-\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65}}{2*2}=\frac{-1+\sqrt{65}}{4}
$