9x^2-14x+3=0

Solution for 9x^2-14x+3=0 equation:

Simplifying
9x2 + -14x + 3 = 0

Reorder the terms:
3 + -14x + 9x2 = 0

Solving
3 + -14x + 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 + -1.555555556x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.555555556x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.555555556x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.555555556x + x2 = 0 + -0.3333333333
-1.555555556x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.555555556x + x2 = -0.3333333333

The x term is -1.555555556x.  Take half its coefficient (-0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
-1.555555556x + 0.6049382720 + x2 = -0.3333333333 + 0.6049382720

Reorder the terms:
0.6049382720 + -1.555555556x + x2 = -0.3333333333 + 0.6049382720

Combine like terms: -0.3333333333 + 0.6049382720 = 0.2716049387
0.6049382720 + -1.555555556x + x2 = 0.2716049387

Factor a perfect square on the left side:
(x + -0.777777778)(x + -0.777777778) = 0.2716049387

Calculate the square root of the right side: 0.521157307

Break this problem into two subproblems by setting 
(x + -0.777777778) equal to 0.521157307 and -0.521157307.

Subproblem 1
x + -0.777777778 = 0.521157307

Simplifying
x + -0.777777778 = 0.521157307

Reorder the terms:
-0.777777778 + x = 0.521157307

Solving
-0.777777778 + x = 0.521157307

Solving for variable 'x'.

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

Add '0.777777778' to each side of the equation.
-0.777777778 + 0.777777778 + x = 0.521157307 + 0.777777778

Combine like terms: -0.777777778 + 0.777777778 = 0.000000000
0.000000000 + x = 0.521157307 + 0.777777778
x = 0.521157307 + 0.777777778

Combine like terms: 0.521157307 + 0.777777778 = 1.298935085
x = 1.298935085

Simplifying
x = 1.298935085

Subproblem 2
x + -0.777777778 = -0.521157307

Simplifying
x + -0.777777778 = -0.521157307

Reorder the terms:
-0.777777778 + x = -0.521157307

Solving
-0.777777778 + x = -0.521157307

Solving for variable 'x'.

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

Add '0.777777778' to each side of the equation.
-0.777777778 + 0.777777778 + x = -0.521157307 + 0.777777778

Combine like terms: -0.777777778 + 0.777777778 = 0.000000000
0.000000000 + x = -0.521157307 + 0.777777778
x = -0.521157307 + 0.777777778

Combine like terms: -0.521157307 + 0.777777778 = 0.256620471
x = 0.256620471

Simplifying
x = 0.256620471

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.298935085, 0.256620471}