12x^2-15x+3.125=0

Solution for 12x^2-15x+3.125=0 equation:

Simplifying
12x2 + -15x + 3.125 = 0

Reorder the terms:
3.125 + -15x + 12x2 = 0

Solving
3.125 + -15x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
0.2604166667 + -1.25x + x2 = 0

Move the constant term to the right:

Add '-0.2604166667' to each side of the equation.
0.2604166667 + -1.25x + -0.2604166667 + x2 = 0 + -0.2604166667

Reorder the terms:
0.2604166667 + -0.2604166667 + -1.25x + x2 = 0 + -0.2604166667

Combine like terms: 0.2604166667 + -0.2604166667 = 0.0000000000
0.0000000000 + -1.25x + x2 = 0 + -0.2604166667
-1.25x + x2 = 0 + -0.2604166667

Combine like terms: 0 + -0.2604166667 = -0.2604166667
-1.25x + x2 = -0.2604166667

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = -0.2604166667 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = -0.2604166667 + 0.390625

Combine like terms: -0.2604166667 + 0.390625 = 0.1302083333
0.390625 + -1.25x + x2 = 0.1302083333

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 0.1302083333

Calculate the square root of the right side: 0.360843918

Break this problem into two subproblems by setting 
(x + -0.625) equal to 0.360843918 and -0.360843918.

Subproblem 1
x + -0.625 = 0.360843918

Simplifying
x + -0.625 = 0.360843918

Reorder the terms:
-0.625 + x = 0.360843918

Solving
-0.625 + x = 0.360843918

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 0.360843918 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 0.360843918 + 0.625
x = 0.360843918 + 0.625

Combine like terms: 0.360843918 + 0.625 = 0.985843918
x = 0.985843918

Simplifying
x = 0.985843918

Subproblem 2
x + -0.625 = -0.360843918

Simplifying
x + -0.625 = -0.360843918

Reorder the terms:
-0.625 + x = -0.360843918

Solving
-0.625 + x = -0.360843918

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -0.360843918 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -0.360843918 + 0.625
x = -0.360843918 + 0.625

Combine like terms: -0.360843918 + 0.625 = 0.264156082
x = 0.264156082

Simplifying
x = 0.264156082

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.985843918, 0.264156082}