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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2+30z+3z-18)=0

We get rid of parentheses

-5z^2+30z+3z-18=0

We add all the numbers together, and all the variables

-5z^2+33z-18=0

a = -5; b = 33; c = -18;
Δ = b2-4ac
Δ = 332-4·(-5)·(-18)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-27}{2*-5}=\frac{-60}{-10}
=+6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+27}{2*-5}=\frac{-6}{-10}
=3/5
$