(3x+1)(2x-8)=2x-8

Solution for (3x+1)(2x-8)=2x-8 equation:

(3x+1)(2x-8)=2x-8

We move all terms to the left:

(3x+1)(2x-8)-(2x-8)=0

We get rid of parentheses

(3x+1)(2x-8)-2x+8=0

We multiply parentheses ..

(+6x^2-24x+2x-8)-2x+8=0

We get rid of parentheses

6x^2-24x+2x-2x-8+8=0

We add all the numbers together, and all the variables

6x^2-24x=0

a = 6; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·6·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*6}=\frac{48}{12}
=4
$