-9x(x+3)=18

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

-9x(x+3)=18

We move all terms to the left:

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

We multiply parentheses

-9x^2-27x-18=0

a = -9; b = -27; c = -18;
Δ = b2-4ac
Δ = -272-4·(-9)·(-18)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9}{2*-9}=\frac{18}{-18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9}{2*-9}=\frac{36}{-18}
=-2
$