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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2z^2+21z+40=0

a = 2; b = 21; c = +40;
Δ = b2-4ac
Δ = 212-4·2·40
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-11}{2*2}=\frac{-32}{4}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+11}{2*2}=\frac{-10}{4}
=-2+1/2
$