y=36/y-9

Solution for y=36/y-9 equation:

y=36/y-9

We move all terms to the left:

y-(36/y-9)=0


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

y∈R


We get rid of parentheses

y-36/y+9=0

We multiply all the terms by the denominator


y*y+9*y-36=0

We add all the numbers together, and all the variables

9y+y*y-36=0

Wy multiply elements

y^2+9y-36=0

a = 1; b = 9; c = -36;
Δ = b2-4ac
Δ = 92-4·1·(-36)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*1}=\frac{-24}{2}
=-12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*1}=\frac{6}{2}
=3
$