5x^2-9x-3=0

Solution for 5x^2-9x-3=0 equation:

Simplifying
5x2 + -9x + -3 = 0

Reorder the terms:
-3 + -9x + 5x2 = 0

Solving
-3 + -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'.
-0.6 + -1.8x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1.8x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1.8x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1.8x + x2 = 0 + 0.6
-1.8x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1.8x + x2 = 0.6

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 = 0.6 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = 0.6 + 0.81

Combine like terms: 0.6 + 0.81 = 1.41
0.81 + -1.8x + x2 = 1.41

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 1.41

Calculate the square root of the right side: 1.187434209

Break this problem into two subproblems by setting 
(x + -0.9) equal to 1.187434209 and -1.187434209.

Subproblem 1
x + -0.9 = 1.187434209

Simplifying
x + -0.9 = 1.187434209

Reorder the terms:
-0.9 + x = 1.187434209

Solving
-0.9 + x = 1.187434209

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 = 1.187434209 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = 1.187434209 + 0.9
x = 1.187434209 + 0.9

Combine like terms: 1.187434209 + 0.9 = 2.087434209
x = 2.087434209

Simplifying
x = 2.087434209

Subproblem 2
x + -0.9 = -1.187434209

Simplifying
x + -0.9 = -1.187434209

Reorder the terms:
-0.9 + x = -1.187434209

Solving
-0.9 + x = -1.187434209

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 = -1.187434209 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = -1.187434209 + 0.9
x = -1.187434209 + 0.9

Combine like terms: -1.187434209 + 0.9 = -0.287434209
x = -0.287434209

Simplifying
x = -0.287434209

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.087434209, -0.287434209}