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

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

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

We multiply parentheses ..

(+5z^2+5z+45z+45)=0

We get rid of parentheses

5z^2+5z+45z+45=0

We add all the numbers together, and all the variables

5z^2+50z+45=0

a = 5; b = 50; c = +45;
Δ = b2-4ac
Δ = 502-4·5·45
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-40}{2*5}=\frac{-90}{10}
=-9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+40}{2*5}=\frac{-10}{10}
=-1
$