(6-2x)(x+9)=0

Solution for (6-2x)(x+9)=0 equation:

(6-2x)(x+9)=0

We add all the numbers together, and all the variables

(-2x+6)(x+9)=0

We multiply parentheses ..

(-2x^2-18x+6x+54)=0

We get rid of parentheses

-2x^2-18x+6x+54=0

We add all the numbers together, and all the variables

-2x^2-12x+54=0

a = -2; b = -12; c = +54;
Δ = b2-4ac
Δ = -122-4·(-2)·54
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*-2}=\frac{36}{-4}
=-9
$