(5z+9)(8+z)=0

Solution for (5z+9)(8+z)=0 equation:

(5z+9)(8+z)=0

We add all the numbers together, and all the variables

(5z+9)(z+8)=0

We multiply parentheses ..

(+5z^2+40z+9z+72)=0

We get rid of parentheses

5z^2+40z+9z+72=0

We add all the numbers together, and all the variables

5z^2+49z+72=0

a = 5; b = 49; c = +72;
Δ = b2-4ac
Δ = 492-4·5·72
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-31}{2*5}=\frac{-80}{10}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+31}{2*5}=\frac{-18}{10}
=-1+4/5
$