(6-z)(3z-8)=0

Solution for (6-z)(3z-8)=0 equation:

(6-z)(3z-8)=0

We add all the numbers together, and all the variables

(-1z+6)(3z-8)=0

We multiply parentheses ..

(-3z^2+8z+18z-48)=0

We get rid of parentheses

-3z^2+8z+18z-48=0

We add all the numbers together, and all the variables

-3z^2+26z-48=0

a = -3; b = 26; c = -48;
Δ = b2-4ac
Δ = 262-4·(-3)·(-48)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10}{2*-3}=\frac{-36}{-6}
=+6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10}{2*-3}=\frac{-16}{-6}
=2+2/3
$