y^2-6y+9=6y

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

y^2-6y+9=6y

We move all terms to the left:

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

We add all the numbers together, and all the variables

y^2-12y+9=0

a = 1; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·1·9
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{3}}{2*1}=\frac{12-6\sqrt{3}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{3}}{2*1}=\frac{12+6\sqrt{3}}{2}
$