3x(2x+9)=12

Solution for 3x(2x+9)=12 equation:

3x(2x+9)=12

We move all terms to the left:

3x(2x+9)-(12)=0

We multiply parentheses

6x^2+27x-12=0

a = 6; b = 27; c = -12;
Δ = b2-4ac
Δ = 272-4·6·(-12)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{113}}{2*6}=\frac{-27-3\sqrt{113}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{113}}{2*6}=\frac{-27+3\sqrt{113}}{12}
$