(-7x^2+x)-(7x^2+5x-4)=

Solution for (-7x^2+x)-(7x^2+5x-4)= equation:

Simplifying
(-7x2 + x) + -1(7x2 + 5x + -4) = 0

Reorder the terms:
(x + -7x2) + -1(7x2 + 5x + -4) = 0

Remove parenthesis around (x + -7x2)
x + -7x2 + -1(7x2 + 5x + -4) = 0

Reorder the terms:
x + -7x2 + -1(-4 + 5x + 7x2) = 0
x + -7x2 + (-4 * -1 + 5x * -1 + 7x2 * -1) = 0
x + -7x2 + (4 + -5x + -7x2) = 0

Reorder the terms:
4 + x + -5x + -7x2 + -7x2 = 0

Combine like terms: x + -5x = -4x
4 + -4x + -7x2 + -7x2 = 0

Combine like terms: -7x2 + -7x2 = -14x2
4 + -4x + -14x2 = 0

Solving
4 + -4x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -2x + -7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -2x + -7x2)' equal to zero and attempt to solve:

Simplifying
2 + -2x + -7x2 = 0

Solving
2 + -2x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.2857142857 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 0.2857142857x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 0.2857142857x + x2 = 0 + 0.2857142857
0.2857142857x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
0.2857142857x + x2 = 0.2857142857

The x term is 0.2857142857x.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x + 0.02040816328 + x2 = 0.2857142857 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = 0.2857142857 + 0.02040816328

Combine like terms: 0.2857142857 + 0.02040816328 = 0.30612244898
0.02040816328 + 0.2857142857x + x2 = 0.30612244898

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = 0.30612244898

Calculate the square root of the right side: 0.553283335

Break this problem into two subproblems by setting 
(x + 0.1428571429) equal to 0.553283335 and -0.553283335.

Subproblem 1
x + 0.1428571429 = 0.553283335

Simplifying
x + 0.1428571429 = 0.553283335

Reorder the terms:
0.1428571429 + x = 0.553283335

Solving
0.1428571429 + x = 0.553283335

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = 0.553283335 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = 0.553283335 + -0.1428571429
x = 0.553283335 + -0.1428571429

Combine like terms: 0.553283335 + -0.1428571429 = 0.4104261921
x = 0.4104261921

Simplifying
x = 0.4104261921

Subproblem 2
x + 0.1428571429 = -0.553283335

Simplifying
x + 0.1428571429 = -0.553283335

Reorder the terms:
0.1428571429 + x = -0.553283335

Solving
0.1428571429 + x = -0.553283335

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = -0.553283335 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = -0.553283335 + -0.1428571429
x = -0.553283335 + -0.1428571429

Combine like terms: -0.553283335 + -0.1428571429 = -0.6961404779
x = -0.6961404779

Simplifying
x = -0.6961404779

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4104261921, -0.6961404779}
Solution
x = {0.4104261921, -0.6961404779}