u^2+3u-26=0

Solution for u^2+3u-26=0 equation:

Simplifying
u2 + 3u + -26 = 0

Reorder the terms:
-26 + 3u + u2 = 0

Solving
-26 + 3u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 3u + 26 + u2 = 0 + 26

Reorder the terms:
-26 + 26 + 3u + u2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 3u + u2 = 0 + 26
3u + u2 = 0 + 26

Combine like terms: 0 + 26 = 26
3u + u2 = 26

The u term is 3u.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3u + 2.25 + u2 = 26 + 2.25

Reorder the terms:
2.25 + 3u + u2 = 26 + 2.25

Combine like terms: 26 + 2.25 = 28.25
2.25 + 3u + u2 = 28.25

Factor a perfect square on the left side:
(u + 1.5)(u + 1.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(u + 1.5) equal to 5.315072906 and -5.315072906.

Subproblem 1
u + 1.5 = 5.315072906

Simplifying
u + 1.5 = 5.315072906

Reorder the terms:
1.5 + u = 5.315072906

Solving
1.5 + u = 5.315072906

Solving for variable 'u'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + u = 5.315072906 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + u = 5.315072906 + -1.5
u = 5.315072906 + -1.5

Combine like terms: 5.315072906 + -1.5 = 3.815072906
u = 3.815072906

Simplifying
u = 3.815072906

Subproblem 2
u + 1.5 = -5.315072906

Simplifying
u + 1.5 = -5.315072906

Reorder the terms:
1.5 + u = -5.315072906

Solving
1.5 + u = -5.315072906

Solving for variable 'u'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + u = -5.315072906 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + u = -5.315072906 + -1.5
u = -5.315072906 + -1.5

Combine like terms: -5.315072906 + -1.5 = -6.815072906
u = -6.815072906

Simplifying
u = -6.815072906

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.815072906, -6.815072906}