2x=4/2x-2

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

2x=4/2x-2

We move all terms to the left:

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


Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

2x-4/2x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+4x-4=0

a = 4; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·4·(-4)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{5}}{2*4}=\frac{-4-4\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{5}}{2*4}=\frac{-4+4\sqrt{5}}{8}
$