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

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

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

We multiply parentheses

27x^2-18x-18=0

a = 27; b = -18; c = -18;
Δ = b2-4ac
Δ = -182-4·27·(-18)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{7}}{2*27}=\frac{18-18\sqrt{7}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{7}}{2*27}=\frac{18+18\sqrt{7}}{54}
$