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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

24x^2-52x-32=0

a = 24; b = -52; c = -32;
Δ = b2-4ac
Δ = -522-4·24·(-32)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-76}{2*24}=\frac{-24}{48}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+76}{2*24}=\frac{128}{48}
=2+2/3
$