15X^2-30X+5=0

Solution for 15X^2-30X+5=0 equation:

Simplifying
15X2 + -30X + 5 = 0

Reorder the terms:
5 + -30X + 15X2 = 0

Solving
5 + -30X + 15X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -6X + 3X2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -6X + 3X2)' equal to zero and attempt to solve:

Simplifying
1 + -6X + 3X2 = 0

Solving
1 + -6X + 3X2 = 0

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

Divide each side by '3'.
0.3333333333 + -2X + X2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2X + -0.3333333333 + X2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2X + X2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2X + X2 = 0 + -0.3333333333
-2X + X2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2X + X2 = -0.3333333333

The X term is -2X.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2X + 1 + X2 = -0.3333333333 + 1

Reorder the terms:
1 + -2X + X2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + -2X + X2 = 0.6666666667

Factor a perfect square on the left side:
(X + -1)(X + -1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(X + -1) equal to 0.816496581 and -0.816496581.

Subproblem 1
X + -1 = 0.816496581

Simplifying
X + -1 = 0.816496581

Reorder the terms:
-1 + X = 0.816496581

Solving
-1 + X = 0.816496581

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X = 0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + X = 0.816496581 + 1
X = 0.816496581 + 1

Combine like terms: 0.816496581 + 1 = 1.816496581
X = 1.816496581

Simplifying
X = 1.816496581

Subproblem 2
X + -1 = -0.816496581

Simplifying
X + -1 = -0.816496581

Reorder the terms:
-1 + X = -0.816496581

Solving
-1 + X = -0.816496581

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X = -0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + X = -0.816496581 + 1
X = -0.816496581 + 1

Combine like terms: -0.816496581 + 1 = 0.183503419
X = 0.183503419

Simplifying
X = 0.183503419

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.816496581, 0.183503419}
Solution
X = {1.816496581, 0.183503419}