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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

24x^2-88x+64=0

a = 24; b = -88; c = +64;
Δ = b2-4ac
Δ = -882-4·24·64
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-40}{2*24}=\frac{48}{48}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+40}{2*24}=\frac{128}{48}
=2+2/3
$