6(y-6)y=9

Solution for 6(y-6)y=9 equation:

6(y-6)y=9

We move all terms to the left:

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

We multiply parentheses

6y^2-36y-9=0

a = 6; b = -36; c = -9;
Δ = b2-4ac
Δ = -362-4·6·(-9)
Δ = 1512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1512}=\sqrt{36*42}=\sqrt{36}*\sqrt{42}=6\sqrt{42}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{42}}{2*6}=\frac{36-6\sqrt{42}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{42}}{2*6}=\frac{36+6\sqrt{42}}{12}
$