12x-15x^2+11x-3=0

Solution for 12x-15x^2+11x-3=0 equation:

Simplifying
12x + -15x2 + 11x + -3 = 0

Reorder the terms:
-3 + 12x + 11x + -15x2 = 0

Combine like terms: 12x + 11x = 23x
-3 + 23x + -15x2 = 0

Solving
-3 + 23x + -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 + -1.533333333x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.533333333x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.533333333x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.533333333x + x2 = 0 + -0.2
-1.533333333x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.533333333x + x2 = -0.2

The x term is -1.533333333x.  Take half its coefficient (-0.7666666665).
Square it (0.5877777775) and add it to both sides.

Add '0.5877777775' to each side of the equation.
-1.533333333x + 0.5877777775 + x2 = -0.2 + 0.5877777775

Reorder the terms:
0.5877777775 + -1.533333333x + x2 = -0.2 + 0.5877777775

Combine like terms: -0.2 + 0.5877777775 = 0.3877777775
0.5877777775 + -1.533333333x + x2 = 0.3877777775

Factor a perfect square on the left side:
(x + -0.7666666665)(x + -0.7666666665) = 0.3877777775

Calculate the square root of the right side: 0.622718056

Break this problem into two subproblems by setting 
(x + -0.7666666665) equal to 0.622718056 and -0.622718056.

Subproblem 1
x + -0.7666666665 = 0.622718056

Simplifying
x + -0.7666666665 = 0.622718056

Reorder the terms:
-0.7666666665 + x = 0.622718056

Solving
-0.7666666665 + x = 0.622718056

Solving for variable 'x'.

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

Add '0.7666666665' to each side of the equation.
-0.7666666665 + 0.7666666665 + x = 0.622718056 + 0.7666666665

Combine like terms: -0.7666666665 + 0.7666666665 = 0.0000000000
0.0000000000 + x = 0.622718056 + 0.7666666665
x = 0.622718056 + 0.7666666665

Combine like terms: 0.622718056 + 0.7666666665 = 1.3893847225
x = 1.3893847225

Simplifying
x = 1.3893847225

Subproblem 2
x + -0.7666666665 = -0.622718056

Simplifying
x + -0.7666666665 = -0.622718056

Reorder the terms:
-0.7666666665 + x = -0.622718056

Solving
-0.7666666665 + x = -0.622718056

Solving for variable 'x'.

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

Add '0.7666666665' to each side of the equation.
-0.7666666665 + 0.7666666665 + x = -0.622718056 + 0.7666666665

Combine like terms: -0.7666666665 + 0.7666666665 = 0.0000000000
0.0000000000 + x = -0.622718056 + 0.7666666665
x = -0.622718056 + 0.7666666665

Combine like terms: -0.622718056 + 0.7666666665 = 0.1439486105
x = 0.1439486105

Simplifying
x = 0.1439486105

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3893847225, 0.1439486105}