3x^2-6x+120=17x-x^2

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Solution for 3x^2-6x+120=17x-x^2 equation: 


Simplifying
3x2 + -6x + 120 = 17x + -1x2

Reorder the terms:
120 + -6x + 3x2 = 17x + -1x2

Solving
120 + -6x + 3x2 = 17x + -1x2

Solving for variable 'x'.

Reorder the terms:
120 + -6x + -17x + 3x2 + x2 = 17x + -1x2 + -17x + x2

Combine like terms: -6x + -17x = -23x
120 + -23x + 3x2 + x2 = 17x + -1x2 + -17x + x2

Combine like terms: 3x2 + x2 = 4x2
120 + -23x + 4x2 = 17x + -1x2 + -17x + x2

Reorder the terms:
120 + -23x + 4x2 = 17x + -17x + -1x2 + x2

Combine like terms: 17x + -17x = 0
120 + -23x + 4x2 = 0 + -1x2 + x2
120 + -23x + 4x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
120 + -23x + 4x2 = 0

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

Divide each side by '4'.
30 + -5.75x + x2 = 0

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -5.75x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -5.75x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -5.75x + x2 = 0 + -30
-5.75x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-5.75x + x2 = -30

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = -30 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = -30 + 8.265625

Combine like terms: -30 + 8.265625 = -21.734375
8.265625 + -5.75x + x2 = -21.734375

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = -21.734375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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