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

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

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

We multiply parentheses ..

(+12x^2+24x-32x-64)=0

We get rid of parentheses

12x^2+24x-32x-64=0

We add all the numbers together, and all the variables

12x^2-8x-64=0

a = 12; b = -8; c = -64;
Δ = b2-4ac
Δ = -82-4·12·(-64)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-56}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+56}{2*12}=\frac{64}{24}
=2+2/3
$