-18=15z-9z(2z-2)

Solution for -18=15z-9z(2z-2) equation:

-18=15z-9z(2z-2)

We move all terms to the left:

-18-(15z-9z(2z-2))=0


We calculate terms in parentheses: -(15z-9z(2z-2)), so:

15z-9z(2z-2)

We multiply parentheses

-18z^2+15z+18z

We add all the numbers together, and all the variables

-18z^2+33z

Back to the equation:

-(-18z^2+33z)


We get rid of parentheses

18z^2-33z-18=0

a = 18; b = -33; c = -18;
Δ = b2-4ac
Δ = -332-4·18·(-18)
Δ = 2385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{265}}{2*18}=\frac{33-3\sqrt{265}}{36}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{265}}{2*18}=\frac{33+3\sqrt{265}}{36}
$