(5z+6)(9+z)=0

Solution for (5z+6)(9+z)=0 equation:

(5z+6)(9+z)=0

We add all the numbers together, and all the variables

(5z+6)(z+9)=0

We multiply parentheses ..

(+5z^2+45z+6z+54)=0

We get rid of parentheses

5z^2+45z+6z+54=0

We add all the numbers together, and all the variables

5z^2+51z+54=0

a = 5; b = 51; c = +54;
Δ = b2-4ac
Δ = 512-4·5·54
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-39}{2*5}=\frac{-90}{10}
=-9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+39}{2*5}=\frac{-12}{10}
=-1+1/5
$