-2n(9n+9)=-144

Solution for -2n(9n+9)=-144 equation:

-2n(9n+9)=-144

We move all terms to the left:

-2n(9n+9)-(-144)=0

We add all the numbers together, and all the variables

-2n(9n+9)+144=0

We multiply parentheses

-18n^2-18n+144=0

a = -18; b = -18; c = +144;
Δ = b2-4ac
Δ = -182-4·(-18)·144
Δ = 10692
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10692}=\sqrt{324*33}=\sqrt{324}*\sqrt{33}=18\sqrt{33}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{33}}{2*-18}=\frac{18-18\sqrt{33}}{-36}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{33}}{2*-18}=\frac{18+18\sqrt{33}}{-36}
$