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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2+20z+6z-24)=0

We get rid of parentheses

-5z^2+20z+6z-24=0

We add all the numbers together, and all the variables

-5z^2+26z-24=0

a = -5; b = 26; c = -24;
Δ = b2-4ac
Δ = 262-4·(-5)·(-24)
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*-5}=\frac{-40}{-10}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+14}{2*-5}=\frac{-12}{-10}
=1+1/5
$