9z(z+8)=-9z-72

Solution for 9z(z+8)=-9z-72 equation:

9z(z+8)=-9z-72

We move all terms to the left:

9z(z+8)-(-9z-72)=0

We multiply parentheses

9z^2+72z-(-9z-72)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

9z^2+81z+72=0

a = 9; b = 81; c = +72;
Δ = b2-4ac
Δ = 812-4·9·72
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-63}{2*9}=\frac{-144}{18}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+63}{2*9}=\frac{-18}{18}
=-1
$