y+6/y-6=3

Solution for y+6/y-6=3 equation:

y+6/y-6=3

We move all terms to the left:

y+6/y-6-(3)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+6/y-9=0

We multiply all the terms by the denominator


y*y-9*y+6=0

We add all the numbers together, and all the variables

-9y+y*y+6=0

Wy multiply elements

y^2-9y+6=0

a = 1; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·1·6
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{57}}{2*1}=\frac{9-\sqrt{57}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*1}=\frac{9+\sqrt{57}}{2}
$