X=1/y-1

Solution for X=1/y-1 equation:

X=1/X-1

We move all terms to the left:

X-(1/X-1)=0


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

X∈R


We get rid of parentheses

X-1/X+1=0

We multiply all the terms by the denominator


X*X+1*X-1=0

We add all the numbers together, and all the variables

X+X*X-1=0

Wy multiply elements

X^2+X-1=0

a = 1; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·1·(-1)
Δ = 5
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{-(1)-\sqrt{5}}{2*1}=\frac{-1-\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*1}=\frac{-1+\sqrt{5}}{2}
$