(y+2)/y+y=74/y

Solution for (y+2)/y+y=74/y equation:

(y+2)/y+y=74/y

We move all terms to the left:

(y+2)/y+y-(74/y)=0


Domain of the equation: y!=0

y∈R



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)/y+y-(+74/y)=0

We add all the numbers together, and all the variables

y+(y+2)/y-(+74/y)=0

We get rid of parentheses

y+(y+2)/y-74/y=0

We multiply all the terms by the denominator


y*y+(y+2)-74=0

Wy multiply elements

y^2+(y+2)-74=0

We get rid of parentheses

y^2+y+2-74=0

We add all the numbers together, and all the variables

y^2+y-72=0

a = 1; b = 1; c = -72;
Δ = b2-4ac
Δ = 12-4·1·(-72)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*1}=\frac{-18}{2}
=-9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*1}=\frac{16}{2}
=8
$