y(4y-9)=9

Solution for y(4y-9)=9 equation:

y(4y-9)=9

We move all terms to the left:

y(4y-9)-(9)=0

We multiply parentheses

4y^2-9y-9=0

a = 4; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·4·(-9)
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*4}=\frac{-6}{8}
=-3/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*4}=\frac{24}{8}
=3
$