(4x^2-2x+8)-(x^2+3x-2)=1

Solution for (4x^2-2x+8)-(x^2+3x-2)=1 equation:

Simplifying
(4x2 + -2x + 8) + -1(x2 + 3x + -2) = 1

Reorder the terms:
(8 + -2x + 4x2) + -1(x2 + 3x + -2) = 1

Remove parenthesis around (8 + -2x + 4x2)
8 + -2x + 4x2 + -1(x2 + 3x + -2) = 1

Reorder the terms:
8 + -2x + 4x2 + -1(-2 + 3x + x2) = 1
8 + -2x + 4x2 + (-2 * -1 + 3x * -1 + x2 * -1) = 1
8 + -2x + 4x2 + (2 + -3x + -1x2) = 1

Reorder the terms:
8 + 2 + -2x + -3x + 4x2 + -1x2 = 1

Combine like terms: 8 + 2 = 10
10 + -2x + -3x + 4x2 + -1x2 = 1

Combine like terms: -2x + -3x = -5x
10 + -5x + 4x2 + -1x2 = 1

Combine like terms: 4x2 + -1x2 = 3x2
10 + -5x + 3x2 = 1

Solving
10 + -5x + 3x2 = 1

Solving for variable 'x'.

Reorder the terms:
10 + -1 + -5x + 3x2 = 1 + -1

Combine like terms: 10 + -1 = 9
9 + -5x + 3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
9 + -5x + 3x2 = 0

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

Divide each side by '3'.
3 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.666666667x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -1.666666667x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.666666667x + x2 = 0 + -3
-1.666666667x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.666666667x + x2 = -3

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -3 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -3 + 0.6944444447

Combine like terms: -3 + 0.6944444447 = -2.3055555553
0.6944444447 + -1.666666667x + x2 = -2.3055555553

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -2.3055555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.