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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2x^2+6x-2x-(3(-4x+2))+12=0


We calculate terms in parentheses: -(3(-4x+2)), so:

3(-4x+2)

We multiply parentheses

-12x+6

Back to the equation:

-(-12x+6)


We add all the numbers together, and all the variables

-2x^2+4x-(-12x+6)+12=0

We get rid of parentheses

-2x^2+4x+12x-6+12=0

We add all the numbers together, and all the variables

-2x^2+16x+6=0

a = -2; b = 16; c = +6;
Δ = b2-4ac
Δ = 162-4·(-2)·6
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{19}}{2*-2}=\frac{-16-4\sqrt{19}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{19}}{2*-2}=\frac{-16+4\sqrt{19}}{-4}
$