3*x+2-1*x-1=7*x^2+x-2

Solution for 3*x+2-1*x-1=7*x^2+x-2 equation:

Simplifying
3x + 2 + -1x + -1 = 7x2 + x + -2

Reorder the terms:
2 + -1 + 3x + -1x = 7x2 + x + -2

Combine like terms: 2 + -1 = 1
1 + 3x + -1x = 7x2 + x + -2

Combine like terms: 3x + -1x = 2x
1 + 2x = 7x2 + x + -2

Reorder the terms:
1 + 2x = -2 + x + 7x2

Solving
1 + 2x = -2 + x + 7x2

Solving for variable 'x'.

Reorder the terms:
1 + 2 + 2x + -1x + -7x2 = -2 + x + 7x2 + 2 + -1x + -7x2

Combine like terms: 1 + 2 = 3
3 + 2x + -1x + -7x2 = -2 + x + 7x2 + 2 + -1x + -7x2

Combine like terms: 2x + -1x = 1x
3 + 1x + -7x2 = -2 + x + 7x2 + 2 + -1x + -7x2

Reorder the terms:
3 + 1x + -7x2 = -2 + 2 + x + -1x + 7x2 + -7x2

Combine like terms: -2 + 2 = 0
3 + 1x + -7x2 = 0 + x + -1x + 7x2 + -7x2
3 + 1x + -7x2 = x + -1x + 7x2 + -7x2

Combine like terms: x + -1x = 0
3 + 1x + -7x2 = 0 + 7x2 + -7x2
3 + 1x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
3 + 1x + -7x2 = 0

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

Divide each side by '-7'.
-0.4285714286 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -0.1428571429x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -0.1428571429x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -0.1428571429x + x2 = 0 + 0.4285714286
-0.1428571429x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-0.1428571429x + x2 = 0.4285714286

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 0.4285714286 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.4285714286 + 0.005102040819

Combine like terms: 0.4285714286 + 0.005102040819 = 0.433673469419
0.005102040819 + -0.1428571429x + x2 = 0.433673469419

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.433673469419

Calculate the square root of the right side: 0.65853889

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.65853889 and -0.65853889.

Subproblem 1
x + -0.07142857145 = 0.65853889

Simplifying
x + -0.07142857145 = 0.65853889

Reorder the terms:
-0.07142857145 + x = 0.65853889

Solving
-0.07142857145 + x = 0.65853889

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = 0.65853889 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = 0.65853889 + 0.07142857145
x = 0.65853889 + 0.07142857145

Combine like terms: 0.65853889 + 0.07142857145 = 0.72996746145
x = 0.72996746145

Simplifying
x = 0.72996746145

Subproblem 2
x + -0.07142857145 = -0.65853889

Simplifying
x + -0.07142857145 = -0.65853889

Reorder the terms:
-0.07142857145 + x = -0.65853889

Solving
-0.07142857145 + x = -0.65853889

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = -0.65853889 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = -0.65853889 + 0.07142857145
x = -0.65853889 + 0.07142857145

Combine like terms: -0.65853889 + 0.07142857145 = -0.58711031855
x = -0.58711031855

Simplifying
x = -0.58711031855

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.72996746145, -0.58711031855}