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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

24x^2-56x+32=0

a = 24; b = -56; c = +32;
Δ = b2-4ac
Δ = -562-4·24·32
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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