(y+1)/y=y

Solution for (y+1)/y=y equation:

(y+1)/y=y

We move all terms to the left:

(y+1)/y-(y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-1y+(y+1)/y=0

We multiply all the terms by the denominator


-1y*y+(y+1)=0

Wy multiply elements

-1y^2+(y+1)=0

We get rid of parentheses

-1y^2+y+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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{5}}{2*-1}=\frac{-1-\sqrt{5}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*-1}=\frac{-1+\sqrt{5}}{-2}
$