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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5y^2+39y+54=0

a = -5; b = 39; c = +54;
Δ = b2-4ac
Δ = 392-4·(-5)·54
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-51}{2*-5}=\frac{-90}{-10}
=+9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+51}{2*-5}=\frac{12}{-10}
=-1+1/5
$