x=4/2x-4

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

x=4/2x-4

We move all terms to the left:

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


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

x-4/2x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+8x-4=0

a = 2; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·2·(-4)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*2}=\frac{-8-4\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*2}=\frac{-8+4\sqrt{6}}{4}
$