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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-18x^2+3x+108x-2=0

We add all the numbers together, and all the variables

-18x^2+111x-2=0

a = -18; b = 111; c = -2;
Δ = b2-4ac
Δ = 1112-4·(-18)·(-2)
Δ = 12177
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:

$\sqrt{\Delta}=\sqrt{12177}=\sqrt{9*1353}=\sqrt{9}*\sqrt{1353}=3\sqrt{1353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-3\sqrt{1353}}{2*-18}=\frac{-111-3\sqrt{1353}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+3\sqrt{1353}}{2*-18}=\frac{-111+3\sqrt{1353}}{-36}
$