-7x^2+x+9=0

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

Simplifying
-7x2 + x + 9 = 0

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

Solving
9 + x + -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 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -0.1428571429x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -0.1428571429x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -0.1428571429x + x2 = 0 + 1.285714286
-0.1428571429x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-0.1428571429x + x2 = 1.285714286

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.1428571429x + 0.25 + x2 = 1.285714286 + 0.25

Reorder the terms:
0.25 + -0.1428571429x + x2 = 1.285714286 + 0.25

Combine like terms: 1.285714286 + 0.25 = 1.535714286
0.25 + -0.1428571429x + x2 = 1.535714286

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.535714286

Calculate the square root of the right side: 1.239239398

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.239239398 and -1.239239398.

Subproblem 1
x + 0.5 = 1.239239398

Simplifying
x + 0.5 = 1.239239398

Reorder the terms:
0.5 + x = 1.239239398

Solving
0.5 + x = 1.239239398

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.239239398 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.239239398 + -0.5
x = 1.239239398 + -0.5

Combine like terms: 1.239239398 + -0.5 = 0.739239398
x = 0.739239398

Simplifying
x = 0.739239398

Subproblem 2
x + 0.5 = -1.239239398

Simplifying
x + 0.5 = -1.239239398

Reorder the terms:
0.5 + x = -1.239239398

Solving
0.5 + x = -1.239239398

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.239239398 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.239239398 + -0.5
x = -1.239239398 + -0.5

Combine like terms: -1.239239398 + -0.5 = -1.739239398
x = -1.739239398

Simplifying
x = -1.739239398

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.739239398, -1.739239398}