4x+12=2x(x+3)

Solution for 4x+12=2x(x+3) equation:

4x+12=2x(x+3)

We move all terms to the left:

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


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

2x(x+3)

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -2; c = +12;
Δ = b2-4ac
Δ = -22-4·(-2)·12
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-2}=\frac{12}{-4}
=-3
$