(8z-11)(2-z)=0

Solution for (8z-11)(2-z)=0 equation:

(8z-11)(2-z)=0

We add all the numbers together, and all the variables

(8z-11)(-1z+2)=0

We multiply parentheses ..

(-8z^2+16z+11z-22)=0

We get rid of parentheses

-8z^2+16z+11z-22=0

We add all the numbers together, and all the variables

-8z^2+27z-22=0

a = -8; b = 27; c = -22;
Δ = b2-4ac
Δ = 272-4·(-8)·(-22)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-5}{2*-8}=\frac{-32}{-16}
=+2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+5}{2*-8}=\frac{-22}{-16}
=1+3/8
$