3(y-6)y=3

Solution for 3(y-6)y=3 equation:

3(y-6)y=3

We move all terms to the left:

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

We multiply parentheses

3y^2-18y-3=0

a = 3; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·3·(-3)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{10}}{2*3}=\frac{18-6\sqrt{10}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{10}}{2*3}=\frac{18+6\sqrt{10}}{6}
$