y=2/y-1

Solution for y=2/y-1 equation:

y=2/y-1

We move all terms to the left:

y-(2/y-1)=0


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

y∈R


We get rid of parentheses

y-2/y+1=0

We multiply all the terms by the denominator


y*y+1*y-2=0

We add all the numbers together, and all the variables

y+y*y-2=0

Wy multiply elements

y^2+y-2=0

a = 1; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·1·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*1}=\frac{-4}{2}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*1}=\frac{2}{2}
=1
$