(x+9)(-2x-3)=0

Solution for (x+9)(-2x-3)=0 equation:

(x+9)(-2x-3)=0

We multiply parentheses ..

(-2x^2-3x-18x-27)=0

We get rid of parentheses

-2x^2-3x-18x-27=0

We add all the numbers together, and all the variables

-2x^2-21x-27=0

a = -2; b = -21; c = -27;
Δ = b2-4ac
Δ = -212-4·(-2)·(-27)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*-2}=\frac{6}{-4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*-2}=\frac{36}{-4}
=-9
$