X=2y/y-1

Solution for X=2y/y-1 equation:

X=2X/X-1

We move all terms to the left:

X-(2X/X-1)=0


Domain of the equation: X-1)!=0

X∈R


We get rid of parentheses

X-2X/X+1=0

We multiply all the terms by the denominator


X*X-2X+1*X=0

We add all the numbers together, and all the variables

-1X+X*X=0

Wy multiply elements

X^2-1X=0

a = 1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*1}=\frac{2}{2}
=1
$