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

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

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

We move all terms to the left:

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

We multiply parentheses

4x-(2(x-8)x)-16+6=0


We calculate terms in parentheses: -(2(x-8)x), so:

2(x-8)x

We multiply parentheses

2x^2-16x

Back to the equation:

-(2x^2-16x)


We add all the numbers together, and all the variables

4x-(2x^2-16x)-10=0

We get rid of parentheses

-2x^2+4x+16x-10=0

We add all the numbers together, and all the variables

-2x^2+20x-10=0

a = -2; b = 20; c = -10;
Δ = b2-4ac
Δ = 202-4·(-2)·(-10)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{5}}{2*-2}=\frac{-20-8\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{5}}{2*-2}=\frac{-20+8\sqrt{5}}{-4}
$