(x+9)(-4x-2)=0

Solution for (x+9)(-4x-2)=0 equation:

(x+9)(-4x-2)=0

We multiply parentheses ..

(-4x^2-2x-36x-18)=0

We get rid of parentheses

-4x^2-2x-36x-18=0

We add all the numbers together, and all the variables

-4x^2-38x-18=0

a = -4; b = -38; c = -18;
Δ = b2-4ac
Δ = -382-4·(-4)·(-18)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-34}{2*-4}=\frac{4}{-8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+34}{2*-4}=\frac{72}{-8}
=-9
$