(5-z)(4z-6)=0

Solution for (5-z)(4z-6)=0 equation:

(5-z)(4z-6)=0

We add all the numbers together, and all the variables

(-1z+5)(4z-6)=0

We multiply parentheses ..

(-4z^2+6z+20z-30)=0

We get rid of parentheses

-4z^2+6z+20z-30=0

We add all the numbers together, and all the variables

-4z^2+26z-30=0

a = -4; b = 26; c = -30;
Δ = b2-4ac
Δ = 262-4·(-4)·(-30)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-14}{2*-4}=\frac{-40}{-8}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+14}{2*-4}=\frac{-12}{-8}
=1+1/2
$