(3z+8)(9-z)=0

Solution for (3z+8)(9-z)=0 equation:

(3z+8)(9-z)=0

We add all the numbers together, and all the variables

(3z+8)(-1z+9)=0

We multiply parentheses ..

(-3z^2+27z-8z+72)=0

We get rid of parentheses

-3z^2+27z-8z+72=0

We add all the numbers together, and all the variables

-3z^2+19z+72=0

a = -3; b = 19; c = +72;
Δ = b2-4ac
Δ = 192-4·(-3)·72
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-35}{2*-3}=\frac{-54}{-6}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+35}{2*-3}=\frac{16}{-6}
=-2+2/3
$