12^3-12x^2+2=0

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

12^3-12x^2+2=0

We add all the numbers together, and all the variables

-12x^2+1730=0

a = -12; b = 0; c = +1730;
Δ = b2-4ac
Δ = 02-4·(-12)·1730
Δ = 83040
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:

$\sqrt{\Delta}=\sqrt{83040}=\sqrt{16*5190}=\sqrt{16}*\sqrt{5190}=4\sqrt{5190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5190}}{2*-12}=\frac{0-4\sqrt{5190}}{-24}
=-\frac{4\sqrt{5190}}{-24}
=-\frac{\sqrt{5190}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5190}}{2*-12}=\frac{0+4\sqrt{5190}}{-24}
=\frac{4\sqrt{5190}}{-24}
=\frac{\sqrt{5190}}{-6}
$