3(3y-1)(6y-5)=0

Solution for 3(3y-1)(6y-5)=0 equation:

3(3y-1)(6y-5)=0

We multiply parentheses ..

3(+18y^2-15y-6y+5)=0

We multiply parentheses

54y^2-45y-18y+15=0

We add all the numbers together, and all the variables

54y^2-63y+15=0

a = 54; b = -63; c = +15;
Δ = b2-4ac
Δ = -632-4·54·15
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-27}{2*54}=\frac{36}{108}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+27}{2*54}=\frac{90}{108}
=5/6
$