15x^2-16x+3=0

Solution for 15x^2-16x+3=0 equation:

Simplifying
15x2 + -16x + 3 = 0

Reorder the terms:
3 + -16x + 15x2 = 0

Solving
3 + -16x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
0.2 + -1.066666667x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.066666667x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.066666667x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.066666667x + x2 = 0 + -0.2
-1.066666667x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.066666667x + x2 = -0.2

The x term is -1.066666667x.  Take half its coefficient (-0.5333333335).
Square it (0.2844444446) and add it to both sides.

Add '0.2844444446' to each side of the equation.
-1.066666667x + 0.2844444446 + x2 = -0.2 + 0.2844444446

Reorder the terms:
0.2844444446 + -1.066666667x + x2 = -0.2 + 0.2844444446

Combine like terms: -0.2 + 0.2844444446 = 0.0844444446
0.2844444446 + -1.066666667x + x2 = 0.0844444446

Factor a perfect square on the left side:
(x + -0.5333333335)(x + -0.5333333335) = 0.0844444446

Calculate the square root of the right side: 0.290593263

Break this problem into two subproblems by setting 
(x + -0.5333333335) equal to 0.290593263 and -0.290593263.

Subproblem 1
x + -0.5333333335 = 0.290593263

Simplifying
x + -0.5333333335 = 0.290593263

Reorder the terms:
-0.5333333335 + x = 0.290593263

Solving
-0.5333333335 + x = 0.290593263

Solving for variable 'x'.

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

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + x = 0.290593263 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + x = 0.290593263 + 0.5333333335
x = 0.290593263 + 0.5333333335

Combine like terms: 0.290593263 + 0.5333333335 = 0.8239265965
x = 0.8239265965

Simplifying
x = 0.8239265965

Subproblem 2
x + -0.5333333335 = -0.290593263

Simplifying
x + -0.5333333335 = -0.290593263

Reorder the terms:
-0.5333333335 + x = -0.290593263

Solving
-0.5333333335 + x = -0.290593263

Solving for variable 'x'.

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

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + x = -0.290593263 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + x = -0.290593263 + 0.5333333335
x = -0.290593263 + 0.5333333335

Combine like terms: -0.290593263 + 0.5333333335 = 0.2427400705
x = 0.2427400705

Simplifying
x = 0.2427400705

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8239265965, 0.2427400705}