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

Solution for (3x-2)(4x+8)=0 equation:

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

We multiply parentheses ..

(+12x^2+24x-8x-16)=0

We get rid of parentheses

12x^2+24x-8x-16=0

We add all the numbers together, and all the variables

12x^2+16x-16=0

a = 12; b = 16; c = -16;
Δ = b2-4ac
Δ = 162-4·12·(-16)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-32}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+32}{2*12}=\frac{16}{24}
=2/3
$