32x^2-5x=60

Solution for 32x^2-5x=60 equation:

Simplifying
32x2 + -5x = 60

Reorder the terms:
-5x + 32x2 = 60

Solving
-5x + 32x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + -5x + 32x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -5x + 32x2 = 0

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

Divide each side by '32'.
-1.875 + -0.15625x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -0.15625x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -0.15625x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -0.15625x + x2 = 0 + 1.875
-0.15625x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-0.15625x + x2 = 1.875

The x term is -0.15625x.  Take half its coefficient (-0.078125).
Square it (0.006103515625) and add it to both sides.

Add '0.006103515625' to each side of the equation.
-0.15625x + 0.006103515625 + x2 = 1.875 + 0.006103515625

Reorder the terms:
0.006103515625 + -0.15625x + x2 = 1.875 + 0.006103515625

Combine like terms: 1.875 + 0.006103515625 = 1.881103515625
0.006103515625 + -0.15625x + x2 = 1.881103515625

Factor a perfect square on the left side:
(x + -0.078125)(x + -0.078125) = 1.881103515625

Calculate the square root of the right side: 1.371533272

Break this problem into two subproblems by setting 
(x + -0.078125) equal to 1.371533272 and -1.371533272.

Subproblem 1
x + -0.078125 = 1.371533272

Simplifying
x + -0.078125 = 1.371533272

Reorder the terms:
-0.078125 + x = 1.371533272

Solving
-0.078125 + x = 1.371533272

Solving for variable 'x'.

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

Add '0.078125' to each side of the equation.
-0.078125 + 0.078125 + x = 1.371533272 + 0.078125

Combine like terms: -0.078125 + 0.078125 = 0.000000
0.000000 + x = 1.371533272 + 0.078125
x = 1.371533272 + 0.078125

Combine like terms: 1.371533272 + 0.078125 = 1.449658272
x = 1.449658272

Simplifying
x = 1.449658272

Subproblem 2
x + -0.078125 = -1.371533272

Simplifying
x + -0.078125 = -1.371533272

Reorder the terms:
-0.078125 + x = -1.371533272

Solving
-0.078125 + x = -1.371533272

Solving for variable 'x'.

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

Add '0.078125' to each side of the equation.
-0.078125 + 0.078125 + x = -1.371533272 + 0.078125

Combine like terms: -0.078125 + 0.078125 = 0.000000
0.000000 + x = -1.371533272 + 0.078125
x = -1.371533272 + 0.078125

Combine like terms: -1.371533272 + 0.078125 = -1.293408272
x = -1.293408272

Simplifying
x = -1.293408272

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.449658272, -1.293408272}