-3x^2-1.51x-.139375=0

Solution for -3x^2-1.51x-.139375=0 equation:

Simplifying
-3x2 + -1.51x + -0.139375 = 0

Reorder the terms:
-0.139375 + -1.51x + -3x2 = 0

Solving
-0.139375 + -1.51x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.04645833333 + 0.5033333333x + x2 = 0

Move the constant term to the right:

Add '-0.04645833333' to each side of the equation.
0.04645833333 + 0.5033333333x + -0.04645833333 + x2 = 0 + -0.04645833333

Reorder the terms:
0.04645833333 + -0.04645833333 + 0.5033333333x + x2 = 0 + -0.04645833333

Combine like terms: 0.04645833333 + -0.04645833333 = 0.00000000000
0.00000000000 + 0.5033333333x + x2 = 0 + -0.04645833333
0.5033333333x + x2 = 0 + -0.04645833333

Combine like terms: 0 + -0.04645833333 = -0.04645833333
0.5033333333x + x2 = -0.04645833333

The x term is 0.5033333333x.  Take half its coefficient (0.2516666667).
Square it (0.06333611113) and add it to both sides.

Add '0.06333611113' to each side of the equation.
0.5033333333x + 0.06333611113 + x2 = -0.04645833333 + 0.06333611113

Reorder the terms:
0.06333611113 + 0.5033333333x + x2 = -0.04645833333 + 0.06333611113

Combine like terms: -0.04645833333 + 0.06333611113 = 0.0168777778
0.06333611113 + 0.5033333333x + x2 = 0.0168777778

Factor a perfect square on the left side:
(x + 0.2516666667)(x + 0.2516666667) = 0.0168777778

Calculate the square root of the right side: 0.129914502

Break this problem into two subproblems by setting 
(x + 0.2516666667) equal to 0.129914502 and -0.129914502.

Subproblem 1
x + 0.2516666667 = 0.129914502

Simplifying
x + 0.2516666667 = 0.129914502

Reorder the terms:
0.2516666667 + x = 0.129914502

Solving
0.2516666667 + x = 0.129914502

Solving for variable 'x'.

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

Add '-0.2516666667' to each side of the equation.
0.2516666667 + -0.2516666667 + x = 0.129914502 + -0.2516666667

Combine like terms: 0.2516666667 + -0.2516666667 = 0.0000000000
0.0000000000 + x = 0.129914502 + -0.2516666667
x = 0.129914502 + -0.2516666667

Combine like terms: 0.129914502 + -0.2516666667 = -0.1217521647
x = -0.1217521647

Simplifying
x = -0.1217521647

Subproblem 2
x + 0.2516666667 = -0.129914502

Simplifying
x + 0.2516666667 = -0.129914502

Reorder the terms:
0.2516666667 + x = -0.129914502

Solving
0.2516666667 + x = -0.129914502

Solving for variable 'x'.

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

Add '-0.2516666667' to each side of the equation.
0.2516666667 + -0.2516666667 + x = -0.129914502 + -0.2516666667

Combine like terms: 0.2516666667 + -0.2516666667 = 0.0000000000
0.0000000000 + x = -0.129914502 + -0.2516666667
x = -0.129914502 + -0.2516666667

Combine like terms: -0.129914502 + -0.2516666667 = -0.3815811687
x = -0.3815811687

Simplifying
x = -0.3815811687

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1217521647, -0.3815811687}