3(x^2-6x-9)=0

Solution for 3(x^2-6x-9)=0 equation:

3(x^2-6x-9)=0

We multiply parentheses

3x^2-18x-27=0

a = 3; b = -18; c = -27;
Δ = b2-4ac
Δ = -182-4·3·(-27)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{2}}{2*3}=\frac{18-18\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{2}}{2*3}=\frac{18+18\sqrt{2}}{6}
$