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

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

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

We multiply parentheses ..

3(+x^2-9x+2x-18)=0

We multiply parentheses

3x^2-27x+6x-54=0

We add all the numbers together, and all the variables

3x^2-21x-54=0

a = 3; b = -21; c = -54;
Δ = b2-4ac
Δ = -212-4·3·(-54)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-33}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+33}{2*3}=\frac{54}{6}
=9
$