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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+5x+4=0

a = -2; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-2)·4
Δ = 57
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{-(5)-\sqrt{57}}{2*-2}=\frac{-5-\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*-2}=\frac{-5+\sqrt{57}}{-4}
$