12x^2-324=0

Solution for 12x^2-324=0 equation:

12x^2-324=0

a = 12; b = 0; c = -324;
Δ = b2-4ac
Δ = 02-4·12·(-324)
Δ = 15552
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:

$\sqrt{\Delta}=\sqrt{15552}=\sqrt{5184*3}=\sqrt{5184}*\sqrt{3}=72\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{3}}{2*12}=\frac{0-72\sqrt{3}}{24}
=-\frac{72\sqrt{3}}{24}
=-3\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{3}}{2*12}=\frac{0+72\sqrt{3}}{24}
=\frac{72\sqrt{3}}{24}
=3\sqrt{3}
$