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

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

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

We move all terms to the left:

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


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

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

-3x^2+2x+6x+4=0

We add all the numbers together, and all the variables

-3x^2+8x+4=0

a = -3; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-3)·4
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*-3}=\frac{-8-4\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*-3}=\frac{-8+4\sqrt{7}}{-6}
$