2(4-3x)(x+12)=0

Solution for 2(4-3x)(x+12)=0 equation:

2(4-3x)(x+12)=0

We add all the numbers together, and all the variables

2(-3x+4)(x+12)=0

We multiply parentheses ..

2(-3x^2-36x+4x+48)=0

We multiply parentheses

-6x^2-72x+8x+96=0

We add all the numbers together, and all the variables

-6x^2-64x+96=0

a = -6; b = -64; c = +96;
Δ = b2-4ac
Δ = -642-4·(-6)·96
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-80}{2*-6}=\frac{-16}{-12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+80}{2*-6}=\frac{144}{-12}
=-12
$