6(x-4)(3x+8)=0

Solution for 6(x-4)(3x+8)=0 equation:

6(x-4)(3x+8)=0

We multiply parentheses ..

6(+3x^2+8x-12x-32)=0

We multiply parentheses

18x^2+48x-72x-192=0

We add all the numbers together, and all the variables

18x^2-24x-192=0

a = 18; b = -24; c = -192;
Δ = b2-4ac
Δ = -242-4·18·(-192)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-120}{2*18}=\frac{-96}{36}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+120}{2*18}=\frac{144}{36}
=4
$