8-12x=x(6x-4)

Solution for 8-12x=x(6x-4) equation:

8-12x=x(6x-4)

We move all terms to the left:

8-12x-(x(6x-4))=0


We calculate terms in parentheses: -(x(6x-4)), so:

x(6x-4)

We multiply parentheses

6x^2-4x

Back to the equation:

-(6x^2-4x)


We get rid of parentheses

-6x^2-12x+4x+8=0

We add all the numbers together, and all the variables

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

a = -6; b = -8; c = +8;
Δ = b2-4ac
Δ = -82-4·(-6)·8
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*-6}=\frac{-8}{-12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*-6}=\frac{24}{-12}
=-2
$