3x^2-5x+10=0.5x+4x+2

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Solution for 3x^2-5x+10=0.5x+4x+2 equation: 


Simplifying
3x2 + -5x + 10 = 0.5x + 4x + 2

Reorder the terms:
10 + -5x + 3x2 = 0.5x + 4x + 2

Reorder the terms:
10 + -5x + 3x2 = 2 + 0.5x + 4x

Combine like terms: 0.5x + 4x = 4.5x
10 + -5x + 3x2 = 2 + 4.5x

Solving
10 + -5x + 3x2 = 2 + 4.5x

Solving for variable 'x'.

Reorder the terms:
10 + -2 + -5x + -4.5x + 3x2 = 2 + 4.5x + -2 + -4.5x

Combine like terms: 10 + -2 = 8
8 + -5x + -4.5x + 3x2 = 2 + 4.5x + -2 + -4.5x

Combine like terms: -5x + -4.5x = -9.5x
8 + -9.5x + 3x2 = 2 + 4.5x + -2 + -4.5x

Reorder the terms:
8 + -9.5x + 3x2 = 2 + -2 + 4.5x + -4.5x

Combine like terms: 2 + -2 = 0
8 + -9.5x + 3x2 = 0 + 4.5x + -4.5x
8 + -9.5x + 3x2 = 4.5x + -4.5x

Combine like terms: 4.5x + -4.5x = 0.0
8 + -9.5x + 3x2 = 0.0

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

Divide each side by '3'.
2.666666667 + -3.166666667x + x2 = 0.0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -3.166666667x + -2.666666667 + x2 = 0.0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -3.166666667x + x2 = 0.0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -3.166666667x + x2 = 0.0 + -2.666666667
-3.166666667x + x2 = 0.0 + -2.666666667

Combine like terms: 0.0 + -2.666666667 = -2.666666667
-3.166666667x + x2 = -2.666666667

The x term is -3.166666667x.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667x + 2.506944447 + x2 = -2.666666667 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667x + x2 = -2.666666667 + 2.506944447

Combine like terms: -2.666666667 + 2.506944447 = -0.15972222
2.506944447 + -3.166666667x + x2 = -0.15972222

Factor a perfect square on the left side:
(x + -1.583333334)(x + -1.583333334) = -0.15972222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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