x(x+2)=2x(x-2)

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

x(x+2)=2x(x-2)

We move all terms to the left:

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

We multiply parentheses

x^2+2x-(2x(x-2))=0


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

2x(x-2)

We multiply parentheses

2x^2-4x

Back to the equation:

-(2x^2-4x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+6x=0

a = -1; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1}=\frac{0}{-2}
=0
$