4x(x-2)=4+2x(x-1)

Solution for 4x(x-2)=4+2x(x-1) equation:

4x(x-2)=4+2x(x-1)

We move all terms to the left:

4x(x-2)-(4+2x(x-1))=0

We multiply parentheses

4x^2-8x-(4+2x(x-1))=0


We calculate terms in parentheses: -(4+2x(x-1)), so:

4+2x(x-1)

determiningTheFunctionDomain
2x(x-1)+4

We multiply parentheses

2x^2-2x+4

Back to the equation:

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


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-6x-4=0

a = 2; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·2·(-4)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{17}}{2*2}=\frac{6-2\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{17}}{2*2}=\frac{6+2\sqrt{17}}{4}
$