3+4x+4=17*x^2-2x+3x-6

Solution for 3+4x+4=17*x^2-2x+3x-6 equation:

Simplifying
3 + 4x + 4 = 17x2 + -2x + 3x + -6

Reorder the terms:
3 + 4 + 4x = 17x2 + -2x + 3x + -6

Combine like terms: 3 + 4 = 7
7 + 4x = 17x2 + -2x + 3x + -6

Reorder the terms:
7 + 4x = -6 + -2x + 3x + 17x2

Combine like terms: -2x + 3x = 1x
7 + 4x = -6 + 1x + 17x2

Solving
7 + 4x = -6 + 1x + 17x2

Solving for variable 'x'.

Reorder the terms:
7 + 6 + 4x + -1x + -17x2 = -6 + 1x + 17x2 + 6 + -1x + -17x2

Combine like terms: 7 + 6 = 13
13 + 4x + -1x + -17x2 = -6 + 1x + 17x2 + 6 + -1x + -17x2

Combine like terms: 4x + -1x = 3x
13 + 3x + -17x2 = -6 + 1x + 17x2 + 6 + -1x + -17x2

Reorder the terms:
13 + 3x + -17x2 = -6 + 6 + 1x + -1x + 17x2 + -17x2

Combine like terms: -6 + 6 = 0
13 + 3x + -17x2 = 0 + 1x + -1x + 17x2 + -17x2
13 + 3x + -17x2 = 1x + -1x + 17x2 + -17x2

Combine like terms: 1x + -1x = 0
13 + 3x + -17x2 = 0 + 17x2 + -17x2
13 + 3x + -17x2 = 17x2 + -17x2

Combine like terms: 17x2 + -17x2 = 0
13 + 3x + -17x2 = 0

Begin completing the square.  Divide all terms by
-17 the coefficient of the squared term: 

Divide each side by '-17'.
-0.7647058824 + -0.1764705882x + x2 = 0

Move the constant term to the right:

Add '0.7647058824' to each side of the equation.
-0.7647058824 + -0.1764705882x + 0.7647058824 + x2 = 0 + 0.7647058824

Reorder the terms:
-0.7647058824 + 0.7647058824 + -0.1764705882x + x2 = 0 + 0.7647058824

Combine like terms: -0.7647058824 + 0.7647058824 = 0.0000000000
0.0000000000 + -0.1764705882x + x2 = 0 + 0.7647058824
-0.1764705882x + x2 = 0 + 0.7647058824

Combine like terms: 0 + 0.7647058824 = 0.7647058824
-0.1764705882x + x2 = 0.7647058824

The x term is -0.1764705882x.  Take half its coefficient (-0.0882352941).
Square it (0.007785467125) and add it to both sides.

Add '0.007785467125' to each side of the equation.
-0.1764705882x + 0.007785467125 + x2 = 0.7647058824 + 0.007785467125

Reorder the terms:
0.007785467125 + -0.1764705882x + x2 = 0.7647058824 + 0.007785467125

Combine like terms: 0.7647058824 + 0.007785467125 = 0.772491349525
0.007785467125 + -0.1764705882x + x2 = 0.772491349525

Factor a perfect square on the left side:
(x + -0.0882352941)(x + -0.0882352941) = 0.772491349525

Calculate the square root of the right side: 0.87891487

Break this problem into two subproblems by setting 
(x + -0.0882352941) equal to 0.87891487 and -0.87891487.

Subproblem 1
x + -0.0882352941 = 0.87891487

Simplifying
x + -0.0882352941 = 0.87891487

Reorder the terms:
-0.0882352941 + x = 0.87891487

Solving
-0.0882352941 + x = 0.87891487

Solving for variable 'x'.

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

Add '0.0882352941' to each side of the equation.
-0.0882352941 + 0.0882352941 + x = 0.87891487 + 0.0882352941

Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000
0.0000000000 + x = 0.87891487 + 0.0882352941
x = 0.87891487 + 0.0882352941

Combine like terms: 0.87891487 + 0.0882352941 = 0.9671501641
x = 0.9671501641

Simplifying
x = 0.9671501641

Subproblem 2
x + -0.0882352941 = -0.87891487

Simplifying
x + -0.0882352941 = -0.87891487

Reorder the terms:
-0.0882352941 + x = -0.87891487

Solving
-0.0882352941 + x = -0.87891487

Solving for variable 'x'.

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

Add '0.0882352941' to each side of the equation.
-0.0882352941 + 0.0882352941 + x = -0.87891487 + 0.0882352941

Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000
0.0000000000 + x = -0.87891487 + 0.0882352941
x = -0.87891487 + 0.0882352941

Combine like terms: -0.87891487 + 0.0882352941 = -0.7906795759
x = -0.7906795759

Simplifying
x = -0.7906795759

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9671501641, -0.7906795759}