14x^2+8x-21=0

Solution for 14x^2+8x-21=0 equation:

Simplifying
14x2 + 8x + -21 = 0

Reorder the terms:
-21 + 8x + 14x2 = 0

Solving
-21 + 8x + 14x2 = 0

Solving for variable 'x'.

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

Divide each side by '14'.
-1.5 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.5714285714x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.5714285714x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.5714285714x + x2 = 0 + 1.5
0.5714285714x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.5714285714x + x2 = 1.5

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 1.5 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 1.5 + 0.08163265305

Combine like terms: 1.5 + 0.08163265305 = 1.58163265305
0.08163265305 + 0.5714285714x + x2 = 1.58163265305

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 1.58163265305

Calculate the square root of the right side: 1.257629776

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 1.257629776 and -1.257629776.

Subproblem 1
x + 0.2857142857 = 1.257629776

Simplifying
x + 0.2857142857 = 1.257629776

Reorder the terms:
0.2857142857 + x = 1.257629776

Solving
0.2857142857 + x = 1.257629776

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = 1.257629776 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 1.257629776 + -0.2857142857
x = 1.257629776 + -0.2857142857

Combine like terms: 1.257629776 + -0.2857142857 = 0.9719154903
x = 0.9719154903

Simplifying
x = 0.9719154903

Subproblem 2
x + 0.2857142857 = -1.257629776

Simplifying
x + 0.2857142857 = -1.257629776

Reorder the terms:
0.2857142857 + x = -1.257629776

Solving
0.2857142857 + x = -1.257629776

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = -1.257629776 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -1.257629776 + -0.2857142857
x = -1.257629776 + -0.2857142857

Combine like terms: -1.257629776 + -0.2857142857 = -1.5433440617
x = -1.5433440617

Simplifying
x = -1.5433440617

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9719154903, -1.5433440617}