6+3(x-9)x=12

Solution for 6+3(x-9)x=12 equation:

6+3(x-9)x=12

We move all terms to the left:

6+3(x-9)x-(12)=0

We add all the numbers together, and all the variables

3(x-9)x-6=0

We multiply parentheses

3x^2-27x-6=0

a = 3; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·3·(-6)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{89}}{2*3}=\frac{27-3\sqrt{89}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{89}}{2*3}=\frac{27+3\sqrt{89}}{6}
$