(9y-3)(31-y)=0

Solution for (9y-3)(31-y)=0 equation:

(9y-3)(31-y)=0

We add all the numbers together, and all the variables

(9y-3)(-1y+31)=0

We multiply parentheses ..

(-9y^2+279y+3y-93)=0

We get rid of parentheses

-9y^2+279y+3y-93=0

We add all the numbers together, and all the variables

-9y^2+282y-93=0

a = -9; b = 282; c = -93;
Δ = b2-4ac
Δ = 2822-4·(-9)·(-93)
Δ = 76176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{76176}=276$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(282)-276}{2*-9}=\frac{-558}{-18}
=+31
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(282)+276}{2*-9}=\frac{-6}{-18}
=1/3
$