-4u^2-2u+120=0

Solution for -4u^2-2u+120=0 equation:

Simplifying
-4u2 + -2u + 120 = 0

Reorder the terms:
120 + -2u + -4u2 = 0

Solving
120 + -2u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + -1u + -2u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(60 + -1u + -2u2)' equal to zero and attempt to solve:

Simplifying
60 + -1u + -2u2 = 0

Solving
60 + -1u + -2u2 = 0

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

Divide each side by '-2'.
-30 + 0.5u + u2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 0.5u + 30 + u2 = 0 + 30

Reorder the terms:
-30 + 30 + 0.5u + u2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 0.5u + u2 = 0 + 30
0.5u + u2 = 0 + 30

Combine like terms: 0 + 30 = 30
0.5u + u2 = 30

The u term is 0.5u.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5u + 0.0625 + u2 = 30 + 0.0625

Reorder the terms:
0.0625 + 0.5u + u2 = 30 + 0.0625

Combine like terms: 30 + 0.0625 = 30.0625
0.0625 + 0.5u + u2 = 30.0625

Factor a perfect square on the left side:
(u + 0.25)(u + 0.25) = 30.0625

Calculate the square root of the right side: 5.48292805

Break this problem into two subproblems by setting 
(u + 0.25) equal to 5.48292805 and -5.48292805.

Subproblem 1
u + 0.25 = 5.48292805

Simplifying
u + 0.25 = 5.48292805

Reorder the terms:
0.25 + u = 5.48292805

Solving
0.25 + u = 5.48292805

Solving for variable 'u'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + u = 5.48292805 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + u = 5.48292805 + -0.25
u = 5.48292805 + -0.25

Combine like terms: 5.48292805 + -0.25 = 5.23292805
u = 5.23292805

Simplifying
u = 5.23292805

Subproblem 2
u + 0.25 = -5.48292805

Simplifying
u + 0.25 = -5.48292805

Reorder the terms:
0.25 + u = -5.48292805

Solving
0.25 + u = -5.48292805

Solving for variable 'u'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + u = -5.48292805 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + u = -5.48292805 + -0.25
u = -5.48292805 + -0.25

Combine like terms: -5.48292805 + -0.25 = -5.73292805
u = -5.73292805

Simplifying
u = -5.73292805

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.23292805, -5.73292805}
Solution
u = {5.23292805, -5.73292805}