-6x^2+5x+6=1.41666

Solution for -6x^2+5x+6=1.41666 equation:

Simplifying
-6x2 + 5x + 6 = 1.41666

Reorder the terms:
6 + 5x + -6x2 = 1.41666

Solving
6 + 5x + -6x2 = 1.41666

Solving for variable 'x'.

Reorder the terms:
6 + -1.41666 + 5x + -6x2 = 1.41666 + -1.41666

Combine like terms: 6 + -1.41666 = 4.58334
4.58334 + 5x + -6x2 = 1.41666 + -1.41666

Combine like terms: 1.41666 + -1.41666 = 0.00000
4.58334 + 5x + -6x2 = 0.00000

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

Divide each side by '-6'.
-0.76389 + -0.8333333333x + x2 = 0.00000

Move the constant term to the right:

Add '0.76389' to each side of the equation.
-0.76389 + -0.8333333333x + 0.76389 + x2 = 0.00000 + 0.76389

Reorder the terms:
-0.76389 + 0.76389 + -0.8333333333x + x2 = 0.00000 + 0.76389

Combine like terms: -0.76389 + 0.76389 = 0.00000
0.00000 + -0.8333333333x + x2 = 0.00000 + 0.76389
-0.8333333333x + x2 = 0.00000 + 0.76389

Combine like terms: 0.00000 + 0.76389 = 0.76389
-0.8333333333x + x2 = 0.76389

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = 0.76389 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 0.76389 + 0.1736111111

Combine like terms: 0.76389 + 0.1736111111 = 0.9375011111
0.1736111111 + -0.8333333333x + x2 = 0.9375011111

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 0.9375011111

Calculate the square root of the right side: 0.96824641

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 0.96824641 and -0.96824641.

Subproblem 1
x + -0.4166666667 = 0.96824641

Simplifying
x + -0.4166666667 = 0.96824641

Reorder the terms:
-0.4166666667 + x = 0.96824641

Solving
-0.4166666667 + x = 0.96824641

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 0.96824641 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 0.96824641 + 0.4166666667
x = 0.96824641 + 0.4166666667

Combine like terms: 0.96824641 + 0.4166666667 = 1.3849130767
x = 1.3849130767

Simplifying
x = 1.3849130767

Subproblem 2
x + -0.4166666667 = -0.96824641

Simplifying
x + -0.4166666667 = -0.96824641

Reorder the terms:
-0.4166666667 + x = -0.96824641

Solving
-0.4166666667 + x = -0.96824641

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -0.96824641 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -0.96824641 + 0.4166666667
x = -0.96824641 + 0.4166666667

Combine like terms: -0.96824641 + 0.4166666667 = -0.5515797433
x = -0.5515797433

Simplifying
x = -0.5515797433

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3849130767, -0.5515797433}