50=-16x^2+96x+60

Solution for 50=-16x^2+96x+60 equation:

Simplifying
50 = -16x2 + 96x + 60

Reorder the terms:
50 = 60 + 96x + -16x2

Solving
50 = 60 + 96x + -16x2

Solving for variable 'x'.

Combine like terms: 50 + -60 = -10
-10 + -96x + 16x2 = 60 + 96x + -16x2 + -60 + -96x + 16x2

Reorder the terms:
-10 + -96x + 16x2 = 60 + -60 + 96x + -96x + -16x2 + 16x2

Combine like terms: 60 + -60 = 0
-10 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2
-10 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2

Combine like terms: 96x + -96x = 0
-10 + -96x + 16x2 = 0 + -16x2 + 16x2
-10 + -96x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-10 + -96x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -48x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -48x + 8x2)' equal to zero and attempt to solve:

Simplifying
-5 + -48x + 8x2 = 0

Solving
-5 + -48x + 8x2 = 0

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

Divide each side by '8'.
-0.625 + -6x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -6x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -6x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -6x + x2 = 0 + 0.625
-6x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-6x + x2 = 0.625

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 0.625 + 9

Reorder the terms:
9 + -6x + x2 = 0.625 + 9

Combine like terms: 0.625 + 9 = 9.625
9 + -6x + x2 = 9.625

Factor a perfect square on the left side:
(x + -3)(x + -3) = 9.625

Calculate the square root of the right side: 3.102418411

Break this problem into two subproblems by setting 
(x + -3) equal to 3.102418411 and -3.102418411.

Subproblem 1
x + -3 = 3.102418411

Simplifying
x + -3 = 3.102418411

Reorder the terms:
-3 + x = 3.102418411

Solving
-3 + x = 3.102418411

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.102418411 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.102418411 + 3
x = 3.102418411 + 3

Combine like terms: 3.102418411 + 3 = 6.102418411
x = 6.102418411

Simplifying
x = 6.102418411

Subproblem 2
x + -3 = -3.102418411

Simplifying
x + -3 = -3.102418411

Reorder the terms:
-3 + x = -3.102418411

Solving
-3 + x = -3.102418411

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.102418411 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.102418411 + 3
x = -3.102418411 + 3

Combine like terms: -3.102418411 + 3 = -0.102418411
x = -0.102418411

Simplifying
x = -0.102418411

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.102418411, -0.102418411}
Solution
x = {6.102418411, -0.102418411}