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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5z^2+42z+16=0

a = 5; b = 42; c = +16;
Δ = b2-4ac
Δ = 422-4·5·16
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-38}{2*5}=\frac{-80}{10}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+38}{2*5}=\frac{-4}{10}
=-2/5
$