(2z+5)(8-z)=0

Solution for (2z+5)(8-z)=0 equation:

(2z+5)(8-z)=0

We add all the numbers together, and all the variables

(2z+5)(-1z+8)=0

We multiply parentheses ..

(-2z^2+16z-5z+40)=0

We get rid of parentheses

-2z^2+16z-5z+40=0

We add all the numbers together, and all the variables

-2z^2+11z+40=0

a = -2; b = 11; c = +40;
Δ = b2-4ac
Δ = 112-4·(-2)·40
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*-2}=\frac{-32}{-4}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*-2}=\frac{10}{-4}
=-2+1/2
$