12x^2-216^3=0

Solution for 12x^2-216^3=0 equation:

12x^2-216^3=0

We add all the numbers together, and all the variables

12x^2-10077696=0

a = 12; b = 0; c = -10077696;
Δ = b2-4ac
Δ = 02-4·12·(-10077696)
Δ = 483729408
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:

$\sqrt{\Delta}=\sqrt{483729408}=\sqrt{241864704*2}=\sqrt{241864704}*\sqrt{2}=15552\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-15552\sqrt{2}}{2*12}=\frac{0-15552\sqrt{2}}{24}
=-\frac{15552\sqrt{2}}{24}
=-648\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15552\sqrt{2}}{2*12}=\frac{0+15552\sqrt{2}}{24}
=\frac{15552\sqrt{2}}{24}
=648\sqrt{2}
$