60=x(2x-1)

Solution for 60=x(2x-1) equation:

Simplifying
60 = x(2x + -1)

Reorder the terms:
60 = x(-1 + 2x)
60 = (-1 * x + 2x * x)
60 = (-1x + 2x2)

Solving
60 = -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
60 + x + -2x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
60 + x + -2x2 = 0 + 2x2 + -2x2
60 + x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
60 + x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-30 + -0.5x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -0.5x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -0.5x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -0.5x + x2 = 0 + 30
-0.5x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-0.5x + x2 = 30

The x term is x.  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.
-0.5x + 0.25 + x2 = 30 + 0.25

Reorder the terms:
0.25 + -0.5x + x2 = 30 + 0.25

Combine like terms: 30 + 0.25 = 30.25
0.25 + -0.5x + x2 = 30.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.5 and -5.5.

Subproblem 1
x + 0.5 = 5.5

Simplifying
x + 0.5 = 5.5

Reorder the terms:
0.5 + x = 5.5

Solving
0.5 + x = 5.5

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 = 5.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.5 + -0.5
x = 5.5 + -0.5

Combine like terms: 5.5 + -0.5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
x + 0.5 = -5.5

Simplifying
x + 0.5 = -5.5

Reorder the terms:
0.5 + x = -5.5

Solving
0.5 + x = -5.5

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 = -5.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.5 + -0.5
x = -5.5 + -0.5

Combine like terms: -5.5 + -0.5 = -6
x = -6

Simplifying
x = -6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, -6}