9(3x^2-4)=0

Solution for 9(3x^2-4)=0 equation:

9(3x^2-4)=0

We multiply parentheses

27x^2-36=0

a = 27; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·27·(-36)
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{3}}{2*27}=\frac{0-36\sqrt{3}}{54}
=-\frac{36\sqrt{3}}{54}
=-\frac{2\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{3}}{2*27}=\frac{0+36\sqrt{3}}{54}
=\frac{36\sqrt{3}}{54}
=\frac{2\sqrt{3}}{3}
$