5x-15x^2+10x=1

Solution for 5x-15x^2+10x=1 equation:

Simplifying
5x + -15x2 + 10x = 1

Reorder the terms:
5x + 10x + -15x2 = 1

Combine like terms: 5x + 10x = 15x
15x + -15x2 = 1

Solving
15x + -15x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 15x + -15x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 15x + -15x2 = 0

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

Divide each side by '-15'.
0.06666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.06666666667' to each side of the equation.
0.06666666667 + -1x + -0.06666666667 + x2 = 0 + -0.06666666667

Reorder the terms:
0.06666666667 + -0.06666666667 + -1x + x2 = 0 + -0.06666666667

Combine like terms: 0.06666666667 + -0.06666666667 = 0.00000000000
0.00000000000 + -1x + x2 = 0 + -0.06666666667
-1x + x2 = 0 + -0.06666666667

Combine like terms: 0 + -0.06666666667 = -0.06666666667
-1x + x2 = -0.06666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.06666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.06666666667 + 0.25

Combine like terms: -0.06666666667 + 0.25 = 0.18333333333
0.25 + -1x + x2 = 0.18333333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.18333333333

Calculate the square root of the right side: 0.428174419

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.428174419 and -0.428174419.

Subproblem 1
x + -0.5 = 0.428174419

Simplifying
x + -0.5 = 0.428174419

Reorder the terms:
-0.5 + x = 0.428174419

Solving
-0.5 + x = 0.428174419

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.428174419 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.428174419 + 0.5
x = 0.428174419 + 0.5

Combine like terms: 0.428174419 + 0.5 = 0.928174419
x = 0.928174419

Simplifying
x = 0.928174419

Subproblem 2
x + -0.5 = -0.428174419

Simplifying
x + -0.5 = -0.428174419

Reorder the terms:
-0.5 + x = -0.428174419

Solving
-0.5 + x = -0.428174419

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.428174419 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.428174419 + 0.5
x = -0.428174419 + 0.5

Combine like terms: -0.428174419 + 0.5 = 0.071825581
x = 0.071825581

Simplifying
x = 0.071825581

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.928174419, 0.071825581}