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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

4x+3x-(2x(x+3))+6=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 add all the numbers together, and all the variables

7x-(2x^2+6x)+6=0

We get rid of parentheses

-2x^2+7x-6x+6=0

We add all the numbers together, and all the variables

-2x^2+x+6=0

a = -2; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-2)·6
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{-(1)-7}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-2}=\frac{6}{-4}
=-1+1/2
$