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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2+30z+4z-24)=0

We get rid of parentheses

-5z^2+30z+4z-24=0

We add all the numbers together, and all the variables

-5z^2+34z-24=0

a = -5; b = 34; c = -24;
Δ = b2-4ac
Δ = 342-4·(-5)·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-26}{2*-5}=\frac{-60}{-10}
=+6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+26}{2*-5}=\frac{-8}{-10}
=4/5
$