(3-z)(5z-6)=0

Solution for (3-z)(5z-6)=0 equation:

(3-z)(5z-6)=0

We add all the numbers together, and all the variables

(-1z+3)(5z-6)=0

We multiply parentheses ..

(-5z^2+6z+15z-18)=0

We get rid of parentheses

-5z^2+6z+15z-18=0

We add all the numbers together, and all the variables

-5z^2+21z-18=0

a = -5; b = 21; c = -18;
Δ = b2-4ac
Δ = 212-4·(-5)·(-18)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-9}{2*-5}=\frac{-30}{-10}
=+3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9}{2*-5}=\frac{-12}{-10}
=1+1/5
$