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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

6x^2-4x-6=0

a = 6; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·6·(-6)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*6}=\frac{4-4\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*6}=\frac{4+4\sqrt{10}}{12}
$