2x(x+2)=x

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

2x(x+2)=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-1x+4x=0

We add all the numbers together, and all the variables

2x^2+3x=0

a = 2; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·2·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*2}=\frac{0}{4}
=0
$