9(6x-2)-3(9x2-3)=0

Solution for 9(6x-2)-3(9x2-3)=0 equation:

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

We multiply parentheses

-27x^2+54x-18+9=0

We add all the numbers together, and all the variables

-27x^2+54x-9=0

a = -27; b = 54; c = -9;
Δ = b2-4ac
Δ = 542-4·(-27)·(-9)
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-18\sqrt{6}}{2*-27}=\frac{-54-18\sqrt{6}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+18\sqrt{6}}{2*-27}=\frac{-54+18\sqrt{6}}{-54}
$