(9-y)(5y-6)=0

Solution for (9-y)(5y-6)=0 equation:

(9-y)(5y-6)=0

We add all the numbers together, and all the variables

(-1y+9)(5y-6)=0

We multiply parentheses ..

(-5y^2+6y+45y-54)=0

We get rid of parentheses

-5y^2+6y+45y-54=0

We add all the numbers together, and all the variables

-5y^2+51y-54=0

a = -5; b = 51; c = -54;
Δ = b2-4ac
Δ = 512-4·(-5)·(-54)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-39}{2*-5}=\frac{-90}{-10}
=+9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+39}{2*-5}=\frac{-12}{-10}
=1+1/5
$