-7x^2+14x+9=0

Solution for -7x^2+14x+9=0 equation:

Simplifying
-7x2 + 14x + 9 = 0

Reorder the terms:
9 + 14x + -7x2 = 0

Solving
9 + 14x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-1.285714286 + -2x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -2x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -2x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.285714286
-2x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-2x + x2 = 1.285714286

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.285714286 + 1

Reorder the terms:
1 + -2x + x2 = 1.285714286 + 1

Combine like terms: 1.285714286 + 1 = 2.285714286
1 + -2x + x2 = 2.285714286

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.285714286

Calculate the square root of the right side: 1.511857892

Break this problem into two subproblems by setting 
(x + -1) equal to 1.511857892 and -1.511857892.

Subproblem 1
x + -1 = 1.511857892

Simplifying
x + -1 = 1.511857892

Reorder the terms:
-1 + x = 1.511857892

Solving
-1 + x = 1.511857892

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.511857892 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.511857892 + 1
x = 1.511857892 + 1

Combine like terms: 1.511857892 + 1 = 2.511857892
x = 2.511857892

Simplifying
x = 2.511857892

Subproblem 2
x + -1 = -1.511857892

Simplifying
x + -1 = -1.511857892

Reorder the terms:
-1 + x = -1.511857892

Solving
-1 + x = -1.511857892

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.511857892 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.511857892 + 1
x = -1.511857892 + 1

Combine like terms: -1.511857892 + 1 = -0.511857892
x = -0.511857892

Simplifying
x = -0.511857892

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.511857892, -0.511857892}