15x^2+2x-6=0

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Solution for 15x^2+2x-6=0 equation: 


Simplifying
15x2 + 2x + -6 = 0

Reorder the terms:
-6 + 2x + 15x2 = 0

Solving
-6 + 2x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-0.4 + 0.1333333333x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.1333333333x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.1333333333x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.1333333333x + x2 = 0 + 0.4
0.1333333333x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.1333333333x + x2 = 0.4

The x term is 0.1333333333x.  Take half its coefficient (0.06666666665).
Square it (0.004444444442) and add it to both sides.

Add '0.004444444442' to each side of the equation.
0.1333333333x + 0.004444444442 + x2 = 0.4 + 0.004444444442

Reorder the terms:
0.004444444442 + 0.1333333333x + x2 = 0.4 + 0.004444444442

Combine like terms: 0.4 + 0.004444444442 = 0.404444444442
0.004444444442 + 0.1333333333x + x2 = 0.404444444442

Factor a perfect square on the left side:
(x + 0.06666666665)(x + 0.06666666665) = 0.404444444442

Calculate the square root of the right side: 0.635959468

Break this problem into two subproblems by setting 
(x + 0.06666666665) equal to 0.635959468 and -0.635959468.


Subproblem 1
x + 0.06666666665 = 0.635959468

Simplifying
x + 0.06666666665 = 0.635959468

Reorder the terms:
0.06666666665 + x = 0.635959468

Solving
0.06666666665 + x = 0.635959468

Solving for variable 'x'.

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

Add '-0.06666666665' to each side of the equation.
0.06666666665 + -0.06666666665 + x = 0.635959468 + -0.06666666665

Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000
0.00000000000 + x = 0.635959468 + -0.06666666665
x = 0.635959468 + -0.06666666665

Combine like terms: 0.635959468 + -0.06666666665 = 0.56929280135
x = 0.56929280135

Simplifying
x = 0.56929280135


Subproblem 2
x + 0.06666666665 = -0.635959468

Simplifying
x + 0.06666666665 = -0.635959468

Reorder the terms:
0.06666666665 + x = -0.635959468

Solving
0.06666666665 + x = -0.635959468

Solving for variable 'x'.

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

Add '-0.06666666665' to each side of the equation.
0.06666666665 + -0.06666666665 + x = -0.635959468 + -0.06666666665

Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000
0.00000000000 + x = -0.635959468 + -0.06666666665
x = -0.635959468 + -0.06666666665

Combine like terms: -0.635959468 + -0.06666666665 = -0.70262613465
x = -0.70262613465

Simplifying
x = -0.70262613465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.56929280135, -0.70262613465}

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