5x^2+6x-9=0

Solution for 5x^2+6x-9=0 equation:

Simplifying
5x2 + 6x + -9 = 0

Reorder the terms:
-9 + 6x + 5x2 = 0

Solving
-9 + 6x + 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 + 1.2x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 1.2x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 1.2x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 1.2x + x2 = 0 + 1.8
1.2x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
1.2x + x2 = 1.8

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 1.8 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 1.8 + 0.36

Combine like terms: 1.8 + 0.36 = 2.16
0.36 + 1.2x + x2 = 2.16

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 2.16

Calculate the square root of the right side: 1.469693846

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1.469693846 and -1.469693846.

Subproblem 1
x + 0.6 = 1.469693846

Simplifying
x + 0.6 = 1.469693846

Reorder the terms:
0.6 + x = 1.469693846

Solving
0.6 + x = 1.469693846

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = 1.469693846 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = 1.469693846 + -0.6
x = 1.469693846 + -0.6

Combine like terms: 1.469693846 + -0.6 = 0.869693846
x = 0.869693846

Simplifying
x = 0.869693846

Subproblem 2
x + 0.6 = -1.469693846

Simplifying
x + 0.6 = -1.469693846

Reorder the terms:
0.6 + x = -1.469693846

Solving
0.6 + x = -1.469693846

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = -1.469693846 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = -1.469693846 + -0.6
x = -1.469693846 + -0.6

Combine like terms: -1.469693846 + -0.6 = -2.069693846
x = -2.069693846

Simplifying
x = -2.069693846

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.869693846, -2.069693846}