(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+42z-54=0

a = -4; b = 42; c = -54;
Δ = b2-4ac
Δ = 422-4·(-4)·(-54)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*-4}=\frac{-72}{-8}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*-4}=\frac{-12}{-8}
=1+1/2
$