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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

9x^2+6x-(6x+4)=0

We get rid of parentheses

9x^2+6x-6x-4=0

We add all the numbers together, and all the variables

9x^2-4=0

a = 9; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·9·(-4)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*9}=\frac{12}{18}
=2/3
$