y^2/y+9=81/y+9

Solution for y^2/y+9=81/y+9 equation:

y^2/y+9=81/y+9

We move all terms to the left:

y^2/y+9-(81/y+9)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: y+9)!=0

y∈R


We get rid of parentheses

y^2/y-81/y-9+9=0

We multiply all the terms by the denominator


y^2-9*y+9*y-81=0

We add all the numbers together, and all the variables

y^2-81=0

a = 1; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·1·(-81)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*1}=\frac{-18}{2}
=-9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*1}=\frac{18}{2}
=9
$