(9y-3)(y-5)=0

Solution for (9y-3)(y-5)=0 equation:

(9y-3)(y-5)=0

We multiply parentheses ..

(+9y^2-45y-3y+15)=0

We get rid of parentheses

9y^2-45y-3y+15=0

We add all the numbers together, and all the variables

9y^2-48y+15=0

a = 9; b = -48; c = +15;
Δ = b2-4ac
Δ = -482-4·9·15
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-42}{2*9}=\frac{6}{18}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+42}{2*9}=\frac{90}{18}
=5
$