x(3x-6)=81

Solution for x(3x-6)=81 equation:

x(3x-6)=81

We move all terms to the left:

x(3x-6)-(81)=0

We multiply parentheses

3x^2-6x-81=0

a = 3; b = -6; c = -81;
Δ = b2-4ac
Δ = -62-4·3·(-81)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{7}}{2*3}=\frac{6-12\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{7}}{2*3}=\frac{6+12\sqrt{7}}{6}
$