3x(2x+4)=9

Solution for 3x(2x+4)=9 equation:

3x(2x+4)=9

We move all terms to the left:

3x(2x+4)-(9)=0

We multiply parentheses

6x^2+12x-9=0

a = 6; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·6·(-9)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{10}}{2*6}=\frac{-12-6\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{10}}{2*6}=\frac{-12+6\sqrt{10}}{12}
$