(3n-9)(9n+18)=0

Solution for (3n-9)(9n+18)=0 equation:

(3n-9)(9n+18)=0

We multiply parentheses ..

(+27n^2+54n-81n-162)=0

We get rid of parentheses

27n^2+54n-81n-162=0

We add all the numbers together, and all the variables

27n^2-27n-162=0

a = 27; b = -27; c = -162;
Δ = b2-4ac
Δ = -272-4·27·(-162)
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-135}{2*27}=\frac{-108}{54}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+135}{2*27}=\frac{162}{54}
=3
$