(2z+7)(8-z)=0

Solution for (2z+7)(8-z)=0 equation:

(2z+7)(8-z)=0

We add all the numbers together, and all the variables

(2z+7)(-1z+8)=0

We multiply parentheses ..

(-2z^2+16z-7z+56)=0

We get rid of parentheses

-2z^2+16z-7z+56=0

We add all the numbers together, and all the variables

-2z^2+9z+56=0

a = -2; b = 9; c = +56;
Δ = b2-4ac
Δ = 92-4·(-2)·56
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-23}{2*-2}=\frac{-32}{-4}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+23}{2*-2}=\frac{14}{-4}
=-3+1/2
$