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

Solution for (2z-1)(8+z)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+2z^2+16z-1z-8)=0

We get rid of parentheses

2z^2+16z-1z-8=0

We add all the numbers together, and all the variables

2z^2+15z-8=0

a = 2; b = 15; c = -8;
Δ = b2-4ac
Δ = 152-4·2·(-8)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-17}{2*2}=\frac{-32}{4}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+17}{2*2}=\frac{2}{4}
=1/2
$