(3x-4)(8x+32)=0

Solution for (3x-4)(8x+32)=0 equation:

(3x-4)(8x+32)=0

We multiply parentheses ..

(+24x^2+96x-32x-128)=0

We get rid of parentheses

24x^2+96x-32x-128=0

We add all the numbers together, and all the variables

24x^2+64x-128=0

a = 24; b = 64; c = -128;
Δ = b2-4ac
Δ = 642-4·24·(-128)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-128}{2*24}=\frac{-192}{48}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+128}{2*24}=\frac{64}{48}
=1+1/3
$