u^2+u-3=30

Solution for u^2+u-3=30 equation:

Simplifying
u2 + u + -3 = 30

Reorder the terms:
-3 + u + u2 = 30

Solving
-3 + u + u2 = 30

Solving for variable 'u'.

Reorder the terms:
-3 + -30 + u + u2 = 30 + -30

Combine like terms: -3 + -30 = -33
-33 + u + u2 = 30 + -30

Combine like terms: 30 + -30 = 0
-33 + u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + u + 33 + u2 = 0 + 33

Reorder the terms:
-33 + 33 + u + u2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + u + u2 = 0 + 33
u + u2 = 0 + 33

Combine like terms: 0 + 33 = 33
u + u2 = 33

The u term is u.  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.
u + 0.25 + u2 = 33 + 0.25

Reorder the terms:
0.25 + u + u2 = 33 + 0.25

Combine like terms: 33 + 0.25 = 33.25
0.25 + u + u2 = 33.25

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(u + 0.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
u + 0.5 = 5.766281297

Simplifying
u + 0.5 = 5.766281297

Reorder the terms:
0.5 + u = 5.766281297

Solving
0.5 + u = 5.766281297

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 5.766281297 + -0.5
u = 5.766281297 + -0.5

Combine like terms: 5.766281297 + -0.5 = 5.266281297
u = 5.266281297

Simplifying
u = 5.266281297

Subproblem 2
u + 0.5 = -5.766281297

Simplifying
u + 0.5 = -5.766281297

Reorder the terms:
0.5 + u = -5.766281297

Solving
0.5 + u = -5.766281297

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -5.766281297 + -0.5
u = -5.766281297 + -0.5

Combine like terms: -5.766281297 + -0.5 = -6.266281297
u = -6.266281297

Simplifying
u = -6.266281297

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.266281297, -6.266281297}