3(x-4)(x+2)=21

Solution for 3(x-4)(x+2)=21 equation:

3(x-4)(x+2)=21

We move all terms to the left:

3(x-4)(x+2)-(21)=0

We multiply parentheses ..

3(+x^2+2x-4x-8)-21=0

We multiply parentheses

3x^2+6x-12x-24-21=0

We add all the numbers together, and all the variables

3x^2-6x-45=0

a = 3; b = -6; c = -45;
Δ = b2-4ac
Δ = -62-4·3·(-45)
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{-(-6)-24}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+24}{2*3}=\frac{30}{6}
=5
$