3p^4-8p^2+6=0

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Solution for 3p^4-8p^2+6=0 equation:


Simplifying
3p4 + -8p2 + 6 = 0

Reorder the terms:
6 + -8p2 + 3p4 = 0

Solving
6 + -8p2 + 3p4 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2 + -2.666666667p2 + p4 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2.666666667p2 + -2 + p4 = 0 + -2

Reorder the terms:
2 + -2 + -2.666666667p2 + p4 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2.666666667p2 + p4 = 0 + -2
-2.666666667p2 + p4 = 0 + -2

Combine like terms: 0 + -2 = -2
-2.666666667p2 + p4 = -2

The p term is -2.666666667p2.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667p2 + 1.777777780 + p4 = -2 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667p2 + p4 = -2 + 1.777777780

Combine like terms: -2 + 1.777777780 = -0.22222222
1.777777780 + -2.666666667p2 + p4 = -0.22222222

Factor a perfect square on the left side:
(p2 + -1.333333334)(p2 + -1.333333334) = -0.22222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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