(4y+4)/y=y

Solution for (4y+4)/y=y equation:

(4y+4)/y=y

We move all terms to the left:

(4y+4)/y-(y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-1y+(4y+4)/y=0

We multiply all the terms by the denominator


-1y*y+(4y+4)=0

Wy multiply elements

-1y^2+(4y+4)=0

We get rid of parentheses

-1y^2+4y+4=0

a = -1; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-1)·4
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-1}=\frac{-4-4\sqrt{2}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-1}=\frac{-4+4\sqrt{2}}{-2}
$