8x-4x(x-3)=2x

Solution for 8x-4x(x-3)=2x equation:

8x-4x(x-3)=2x

We move all terms to the left:

8x-4x(x-3)-(2x)=0

We add all the numbers together, and all the variables

6x-4x(x-3)=0

We multiply parentheses

-4x^2+6x+12x=0

We add all the numbers together, and all the variables

-4x^2+18x=0

a = -4; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-4)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-4}=\frac{-36}{-8}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-4}=\frac{0}{-8}
=0
$