x^4-17*x^3+78*X^2-84*x+20=0

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Solution for x^4-17*x^3+78*X^2-84*x+20=0 equation: 


Simplifying
x4 + -17x3 + 78X2 + -84x + 20 = 0

Reorder the terms:
20 + 78X2 + -84x + -17x3 + x4 = 0

Solving
20 + 78X2 + -84x + -17x3 + x4 = 0

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-20' to each side of the equation.
20 + 78X2 + -84x + -17x3 + -20 + x4 = 0 + -20

Reorder the terms:
20 + -20 + 78X2 + -84x + -17x3 + x4 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 78X2 + -84x + -17x3 + x4 = 0 + -20
78X2 + -84x + -17x3 + x4 = 0 + -20

Combine like terms: 0 + -20 = -20
78X2 + -84x + -17x3 + x4 = -20

Add '84x' to each side of the equation.
78X2 + -84x + -17x3 + 84x + x4 = -20 + 84x

Reorder the terms:
78X2 + -84x + 84x + -17x3 + x4 = -20 + 84x

Combine like terms: -84x + 84x = 0
78X2 + 0 + -17x3 + x4 = -20 + 84x
78X2 + -17x3 + x4 = -20 + 84x

Add '17x3' to each side of the equation.
78X2 + -17x3 + 17x3 + x4 = -20 + 84x + 17x3

Combine like terms: -17x3 + 17x3 = 0
78X2 + 0 + x4 = -20 + 84x + 17x3
78X2 + x4 = -20 + 84x + 17x3

Add '-1x4' to each side of the equation.
78X2 + x4 + -1x4 = -20 + 84x + 17x3 + -1x4

Combine like terms: x4 + -1x4 = 0
78X2 + 0 = -20 + 84x + 17x3 + -1x4
78X2 = -20 + 84x + 17x3 + -1x4

Divide each side by '78'.
X2 = -0.2564102564 + 1.076923077x + 0.2179487179x3 + -0.01282051282x4

Simplifying
X2 = -0.2564102564 + 1.076923077x + 0.2179487179x3 + -0.01282051282x4

Reorder the terms:
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = -0.2564102564 + 1.076923077x + 0.2179487179x3 + -0.01282051282x4 + 0.2564102564 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4

Reorder the terms:
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = -0.2564102564 + 0.2564102564 + 1.076923077x + -1.076923077x + 0.2179487179x3 + -0.2179487179x3 + -0.01282051282x4 + 0.01282051282x4

Combine like terms: -0.2564102564 + 0.2564102564 = 0.0000000000
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = 0.0000000000 + 1.076923077x + -1.076923077x + 0.2179487179x3 + -0.2179487179x3 + -0.01282051282x4 + 0.01282051282x4
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = 1.076923077x + -1.076923077x + 0.2179487179x3 + -0.2179487179x3 + -0.01282051282x4 + 0.01282051282x4

Combine like terms: 1.076923077x + -1.076923077x = 0.000000000
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = 0.000000000 + 0.2179487179x3 + -0.2179487179x3 + -0.01282051282x4 + 0.01282051282x4
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = 0.2179487179x3 + -0.2179487179x3 + -0.01282051282x4 + 0.01282051282x4

Combine like terms: 0.2179487179x3 + -0.2179487179x3 = 0.0000000000
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = 0.0000000000 + -0.01282051282x4 + 0.01282051282x4
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = -0.01282051282x4 + 0.01282051282x4

Combine like terms: -0.01282051282x4 + 0.01282051282x4 = 0.00000000000
0.2564102564 + X2 + -1.076923077x + -0.2179487179x3 + 0.01282051282x4 = 0.00000000000

The solution to this equation could not be determined.

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