9x^2-7x-3=0

Solution for 9x^2-7x-3=0 equation:

Simplifying
9x2 + -7x + -3 = 0

Reorder the terms:
-3 + -7x + 9x2 = 0

Solving
-3 + -7x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.3333333333 + -0.7777777778x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.7777777778x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.7777777778x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.7777777778x + x2 = 0 + 0.3333333333
-0.7777777778x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.7777777778x + x2 = 0.3333333333

The x term is -0.7777777778x.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778x + 0.1512345679 + x2 = 0.3333333333 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778x + x2 = 0.3333333333 + 0.1512345679

Combine like terms: 0.3333333333 + 0.1512345679 = 0.4845679012
0.1512345679 + -0.7777777778x + x2 = 0.4845679012

Factor a perfect square on the left side:
(x + -0.3888888889)(x + -0.3888888889) = 0.4845679012

Calculate the square root of the right side: 0.696109116

Break this problem into two subproblems by setting 
(x + -0.3888888889) equal to 0.696109116 and -0.696109116.

Subproblem 1
x + -0.3888888889 = 0.696109116

Simplifying
x + -0.3888888889 = 0.696109116

Reorder the terms:
-0.3888888889 + x = 0.696109116

Solving
-0.3888888889 + x = 0.696109116

Solving for variable 'x'.

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

Add '0.3888888889' to each side of the equation.
-0.3888888889 + 0.3888888889 + x = 0.696109116 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + x = 0.696109116 + 0.3888888889
x = 0.696109116 + 0.3888888889

Combine like terms: 0.696109116 + 0.3888888889 = 1.0849980049
x = 1.0849980049

Simplifying
x = 1.0849980049

Subproblem 2
x + -0.3888888889 = -0.696109116

Simplifying
x + -0.3888888889 = -0.696109116

Reorder the terms:
-0.3888888889 + x = -0.696109116

Solving
-0.3888888889 + x = -0.696109116

Solving for variable 'x'.

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

Add '0.3888888889' to each side of the equation.
-0.3888888889 + 0.3888888889 + x = -0.696109116 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + x = -0.696109116 + 0.3888888889
x = -0.696109116 + 0.3888888889

Combine like terms: -0.696109116 + 0.3888888889 = -0.3072202271
x = -0.3072202271

Simplifying
x = -0.3072202271

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0849980049, -0.3072202271}