(3y-1)(9-y)=0

Solution for (3y-1)(9-y)=0 equation:

(3y-1)(9-y)=0

We add all the numbers together, and all the variables

(3y-1)(-1y+9)=0

We multiply parentheses ..

(-3y^2+27y+y-9)=0

We get rid of parentheses

-3y^2+27y+y-9=0

We add all the numbers together, and all the variables

-3y^2+28y-9=0

a = -3; b = 28; c = -9;
Δ = b2-4ac
Δ = 282-4·(-3)·(-9)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-26}{2*-3}=\frac{-54}{-6}
=+9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+26}{2*-3}=\frac{-2}{-6}
=1/3
$