3y(y-6)=36

Solution for 3y(y-6)=36 equation:

3y(y-6)=36

We move all terms to the left:

3y(y-6)-(36)=0

We multiply parentheses

3y^2-18y-36=0

a = 3; b = -18; c = -36;
Δ = b2-4ac
Δ = -182-4·3·(-36)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{21}}{2*3}=\frac{18-6\sqrt{21}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{21}}{2*3}=\frac{18+6\sqrt{21}}{6}
$