2(x-6)-4x=-4x(x-3)-8

Solution for 2(x-6)-4x=-4x(x-3)-8 equation:

2(x-6)-4x=-4x(x-3)-8

We move all terms to the left:

2(x-6)-4x-(-4x(x-3)-8)=0

We add all the numbers together, and all the variables

-4x+2(x-6)-(-4x(x-3)-8)=0

We multiply parentheses

-4x+2x-(-4x(x-3)-8)-12=0


We calculate terms in parentheses: -(-4x(x-3)-8), so:

-4x(x-3)-8

We multiply parentheses

-4x^2+12x-8

Back to the equation:

-(-4x^2+12x-8)


We add all the numbers together, and all the variables

-(-4x^2+12x-8)-2x-12=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-14x-4=0

a = 4; b = -14; c = -4;
Δ = b2-4ac
Δ = -142-4·4·(-4)
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*4}=\frac{14-2\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*4}=\frac{14+2\sqrt{65}}{8}
$