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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2x+8(x-4)), so:

2x+8(x-4)

We multiply parentheses

2x+8x-32

We add all the numbers together, and all the variables

10x-32

Back to the equation:

-(10x-32)


We get rid of parentheses

4x^2-16x-10x+32=0

We add all the numbers together, and all the variables

4x^2-26x+32=0

a = 4; b = -26; c = +32;
Δ = b2-4ac
Δ = -262-4·4·32
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{41}}{2*4}=\frac{26-2\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{41}}{2*4}=\frac{26+2\sqrt{41}}{8}
$