-4x^2-17x+6=0

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Solution for -4x^2-17x+6=0 equation: 


Simplifying
-4x2 + -17x + 6 = 0

Reorder the terms:
6 + -17x + -4x2 = 0

Solving
6 + -17x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.5 + 4.25x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4.25x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4.25x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4.25x + x2 = 0 + 1.5
4.25x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4.25x + x2 = 1.5

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = 1.5 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 1.5 + 4.515625

Combine like terms: 1.5 + 4.515625 = 6.015625
4.515625 + 4.25x + x2 = 6.015625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 6.015625

Calculate the square root of the right side: 2.452677109

Break this problem into two subproblems by setting 
(x + 2.125) equal to 2.452677109 and -2.452677109.


Subproblem 1
x + 2.125 = 2.452677109

Simplifying
x + 2.125 = 2.452677109

Reorder the terms:
2.125 + x = 2.452677109

Solving
2.125 + x = 2.452677109

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = 2.452677109 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 2.452677109 + -2.125
x = 2.452677109 + -2.125

Combine like terms: 2.452677109 + -2.125 = 0.327677109
x = 0.327677109

Simplifying
x = 0.327677109


Subproblem 2
x + 2.125 = -2.452677109

Simplifying
x + 2.125 = -2.452677109

Reorder the terms:
2.125 + x = -2.452677109

Solving
2.125 + x = -2.452677109

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = -2.452677109 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -2.452677109 + -2.125
x = -2.452677109 + -2.125

Combine like terms: -2.452677109 + -2.125 = -4.577677109
x = -4.577677109

Simplifying
x = -4.577677109


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.327677109, -4.577677109}

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