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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

2(-1z^2+8z-7z+56)=0

We multiply parentheses

-2z^2+16z-14z+112=0

We add all the numbers together, and all the variables

-2z^2+2z+112=0

a = -2; b = 2; c = +112;
Δ = b2-4ac
Δ = 22-4·(-2)·112
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-30}{2*-2}=\frac{-32}{-4}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+30}{2*-2}=\frac{28}{-4}
=-7
$