(5x^2-3x+1)-(2x^2-4x-2)=0

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Solution for (5x^2-3x+1)-(2x^2-4x-2)=0 equation: 


Simplifying
(5x2 + -3x + 1) + -1(2x2 + -4x + -2) = 0

Reorder the terms:
(1 + -3x + 5x2) + -1(2x2 + -4x + -2) = 0

Remove parenthesis around (1 + -3x + 5x2)
1 + -3x + 5x2 + -1(2x2 + -4x + -2) = 0

Reorder the terms:
1 + -3x + 5x2 + -1(-2 + -4x + 2x2) = 0
1 + -3x + 5x2 + (-2 * -1 + -4x * -1 + 2x2 * -1) = 0
1 + -3x + 5x2 + (2 + 4x + -2x2) = 0

Reorder the terms:
1 + 2 + -3x + 4x + 5x2 + -2x2 = 0

Combine like terms: 1 + 2 = 3
3 + -3x + 4x + 5x2 + -2x2 = 0

Combine like terms: -3x + 4x = 1x
3 + 1x + 5x2 + -2x2 = 0

Combine like terms: 5x2 + -2x2 = 3x2
3 + 1x + 3x2 = 0

Solving
3 + 1x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
1 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.3333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 0.3333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.3333333333x + x2 = 0 + -1
0.3333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.3333333333x + x2 = -1

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = -1 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = -1 + 0.02777777779

Combine like terms: -1 + 0.02777777779 = -0.97222222221
0.02777777779 + 0.3333333333x + x2 = -0.97222222221

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = -0.97222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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