6y(4y-9)=0

Solution for 6y(4y-9)=0 equation:

6y(4y-9)=0

We multiply parentheses

24y^2-54y=0

a = 24; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·24·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*24}=\frac{0}{48}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*24}=\frac{108}{48}
=2+1/4
$