4x+6=2+3x(x+2)

Solution for 4x+6=2+3x(x+2) equation:

4x+6=2+3x(x+2)

We move all terms to the left:

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


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

2+3x(x+2)

determiningTheFunctionDomain
3x(x+2)+2

We multiply parentheses

3x^2+6x+2

Back to the equation:

-(3x^2+6x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = -2; c = +4;
Δ = b2-4ac
Δ = -22-4·(-3)·4
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*-3}=\frac{2-2\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*-3}=\frac{2+2\sqrt{13}}{-6}
$