(3y+4)(9-y)=0

Solution for (3y+4)(9-y)=0 equation:

(3y+4)(9-y)=0

We add all the numbers together, and all the variables

(3y+4)(-1y+9)=0

We multiply parentheses ..

(-3y^2+27y-4y+36)=0

We get rid of parentheses

-3y^2+27y-4y+36=0

We add all the numbers together, and all the variables

-3y^2+23y+36=0

a = -3; b = 23; c = +36;
Δ = b2-4ac
Δ = 232-4·(-3)·36
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-31}{2*-3}=\frac{-54}{-6}
=+9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+31}{2*-3}=\frac{8}{-6}
=-1+1/3
$