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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x+2x(x-1)

We multiply parentheses

2x^2+x-2x

We add all the numbers together, and all the variables

2x^2-1x

Back to the equation:

-(2x^2-1x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-7x=0

a = 2; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*2}=\frac{14}{4}
=3+1/2
$