5x^2+9x-9=0

Solution for 5x^2+9x-9=0 equation:

Simplifying
5x2 + 9x + -9 = 0

Reorder the terms:
-9 + 9x + 5x2 = 0

Solving
-9 + 9x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.8 + 1.8x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 1.8x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 1.8x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 1.8x + x2 = 0 + 1.8
1.8x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
1.8x + x2 = 1.8

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 1.8 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 1.8 + 0.81

Combine like terms: 1.8 + 0.81 = 2.61
0.81 + 1.8x + x2 = 2.61

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 2.61

Calculate the square root of the right side: 1.615549442

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1.615549442 and -1.615549442.

Subproblem 1
x + 0.9 = 1.615549442

Simplifying
x + 0.9 = 1.615549442

Reorder the terms:
0.9 + x = 1.615549442

Solving
0.9 + x = 1.615549442

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 1.615549442 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 1.615549442 + -0.9
x = 1.615549442 + -0.9

Combine like terms: 1.615549442 + -0.9 = 0.715549442
x = 0.715549442

Simplifying
x = 0.715549442

Subproblem 2
x + 0.9 = -1.615549442

Simplifying
x + 0.9 = -1.615549442

Reorder the terms:
0.9 + x = -1.615549442

Solving
0.9 + x = -1.615549442

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -1.615549442 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -1.615549442 + -0.9
x = -1.615549442 + -0.9

Combine like terms: -1.615549442 + -0.9 = -2.515549442
x = -2.515549442

Simplifying
x = -2.515549442

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.715549442, -2.515549442}