6x^2-7x-4=0

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Solution for 6x^2-7x-4=0 equation: 


Simplifying
6x2 + -7x + -4 = 0

Reorder the terms:
-4 + -7x + 6x2 = 0

Solving
-4 + -7x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.6666666667 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1.166666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1.166666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1.166666667x + x2 = 0 + 0.6666666667
-1.166666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1.166666667x + x2 = 0.6666666667

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 0.6666666667 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 0.6666666667 + 0.3402777780

Combine like terms: 0.6666666667 + 0.3402777780 = 1.0069444447
0.3402777780 + -1.166666667x + x2 = 1.0069444447

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 1.0069444447

Calculate the square root of the right side: 1.003466215

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 1.003466215 and -1.003466215.


Subproblem 1
x + -0.5833333335 = 1.003466215

Simplifying
x + -0.5833333335 = 1.003466215

Reorder the terms:
-0.5833333335 + x = 1.003466215

Solving
-0.5833333335 + x = 1.003466215

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = 1.003466215 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = 1.003466215 + 0.5833333335
x = 1.003466215 + 0.5833333335

Combine like terms: 1.003466215 + 0.5833333335 = 1.5867995485
x = 1.5867995485

Simplifying
x = 1.5867995485


Subproblem 2
x + -0.5833333335 = -1.003466215

Simplifying
x + -0.5833333335 = -1.003466215

Reorder the terms:
-0.5833333335 + x = -1.003466215

Solving
-0.5833333335 + x = -1.003466215

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = -1.003466215 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = -1.003466215 + 0.5833333335
x = -1.003466215 + 0.5833333335

Combine like terms: -1.003466215 + 0.5833333335 = -0.4201328815
x = -0.4201328815

Simplifying
x = -0.4201328815


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5867995485, -0.4201328815}

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