2y+7=y(8+y)/y

Solution for 2y+7=y(8+y)/y equation:

2y+7=y(8+y)/y

We move all terms to the left:

2y+7-(y(8+y)/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

2y-(y(y+8)/y)+7=0

We multiply all the terms by the denominator


2y*y)-(y(y+8)+7*y)=0

Wy multiply elements

2y^2+7y=0

a = 2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*2}=\frac{-14}{4}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*2}=\frac{0}{4}
=0
$