(2+y)/4(2+)=(-2+1/y)

Solution for (2+y)/4(2+)=(-2+1/y) equation:

(2+y)/4(2+)=(-2+1/y)

We move all terms to the left:

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


Domain of the equation: y))!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(y+2)/40-((1/y-2))=0

We calculate fractions


(y^2+2y)/40y+()/40y=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

(y^2+2y)=0

We get rid of parentheses

y^2+2y=0

a = 1; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·1·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*1}=\frac{-4}{2}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*1}=\frac{0}{2}
=0
$