2x(2x+4)=4x(3x+1)

Solution for 2x(2x+4)=4x(3x+1) equation:

2x(2x+4)=4x(3x+1)

We move all terms to the left:

2x(2x+4)-(4x(3x+1))=0

We multiply parentheses

4x^2+8x-(4x(3x+1))=0


We calculate terms in parentheses: -(4x(3x+1)), so:

4x(3x+1)

We multiply parentheses

12x^2+4x

Back to the equation:

-(12x^2+4x)


We get rid of parentheses

4x^2-12x^2+8x-4x=0

We add all the numbers together, and all the variables

-8x^2+4x=0

a = -8; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-8)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-8}=\frac{-8}{-16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-8}=\frac{0}{-16}
=0
$