(9-z)(4z+6)=0

Solution for (9-z)(4z+6)=0 equation:

(9-z)(4z+6)=0

We add all the numbers together, and all the variables

(-1z+9)(4z+6)=0

We multiply parentheses ..

(-4z^2-6z+36z+54)=0

We get rid of parentheses

-4z^2-6z+36z+54=0

We add all the numbers together, and all the variables

-4z^2+30z+54=0

a = -4; b = 30; c = +54;
Δ = b2-4ac
Δ = 302-4·(-4)·54
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-42}{2*-4}=\frac{-72}{-8}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+42}{2*-4}=\frac{12}{-8}
=-1+1/2
$