9z^2=-72+81z

Solution for 9z^2=-72+81z equation:

9z^2=-72+81z

We move all terms to the left:

9z^2-(-72+81z)=0

We add all the numbers together, and all the variables

9z^2-(81z-72)=0

We get rid of parentheses

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