y(6y-72)-8(6y-72)=0

Solution for y(6y-72)-8(6y-72)=0 equation:

y(6y-72)-8(6y-72)=0

We multiply parentheses

6y^2-72y-48y+576=0

We add all the numbers together, and all the variables

6y^2-120y+576=0

a = 6; b = -120; c = +576;
Δ = b2-4ac
Δ = -1202-4·6·576
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24}{2*6}=\frac{96}{12}
=8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24}{2*6}=\frac{144}{12}
=12
$