2/y+1+1=2y

Solution for 2/y+1+1=2y equation:

2/y+1+1=2y

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-2y+2/y+2=0

We multiply all the terms by the denominator


-2y*y+2*y+2=0

We add all the numbers together, and all the variables

2y-2y*y+2=0

Wy multiply elements

-2y^2+2y+2=0

a = -2; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-2)·2
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*-2}=\frac{-2-2\sqrt{5}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*-2}=\frac{-2+2\sqrt{5}}{-4}
$