(2z-3)(9-z)=0

Solution for (2z-3)(9-z)=0 equation:

(2z-3)(9-z)=0

We add all the numbers together, and all the variables

(2z-3)(-1z+9)=0

We multiply parentheses ..

(-2z^2+18z+3z-27)=0

We get rid of parentheses

-2z^2+18z+3z-27=0

We add all the numbers together, and all the variables

-2z^2+21z-27=0

a = -2; b = 21; c = -27;
Δ = b2-4ac
Δ = 212-4·(-2)·(-27)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*-2}=\frac{-36}{-4}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*-2}=\frac{-6}{-4}
=1+1/2
$