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

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

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

We multiply parentheses ..

(+32x^2+24x-64x-48)=0

We get rid of parentheses

32x^2+24x-64x-48=0

We add all the numbers together, and all the variables

32x^2-40x-48=0

a = 32; b = -40; c = -48;
Δ = b2-4ac
Δ = -402-4·32·(-48)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-88}{2*32}=\frac{-48}{64}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+88}{2*32}=\frac{128}{64}
=2
$