-6y=9y^2

Solution for -6y=9y^2 equation:

-6y=9y^2

We move all terms to the left:

-6y-(9y^2)=0

determiningTheFunctionDomain
-9y^2-6y=0

a = -9; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-9)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-9}=\frac{0}{-18}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-9}=\frac{12}{-18}
=-2/3
$