2u^2+8u-9=0

Solution for 2u^2+8u-9=0 equation:

Simplifying
2u2 + 8u + -9 = 0

Reorder the terms:
-9 + 8u + 2u2 = 0

Solving
-9 + 8u + 2u2 = 0

Solving for variable 'u'.

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

Divide each side by '2'.
-4.5 + 4u + u2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 4u + 4.5 + u2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 4u + u2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 4u + u2 = 0 + 4.5
4u + u2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
4u + u2 = 4.5

The u term is 4u.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4u + 4 + u2 = 4.5 + 4

Reorder the terms:
4 + 4u + u2 = 4.5 + 4

Combine like terms: 4.5 + 4 = 8.5
4 + 4u + u2 = 8.5

Factor a perfect square on the left side:
(u + 2)(u + 2) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(u + 2) equal to 2.915475947 and -2.915475947.

Subproblem 1
u + 2 = 2.915475947

Simplifying
u + 2 = 2.915475947

Reorder the terms:
2 + u = 2.915475947

Solving
2 + u = 2.915475947

Solving for variable 'u'.

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

Add '-2' to each side of the equation.
2 + -2 + u = 2.915475947 + -2

Combine like terms: 2 + -2 = 0
0 + u = 2.915475947 + -2
u = 2.915475947 + -2

Combine like terms: 2.915475947 + -2 = 0.915475947
u = 0.915475947

Simplifying
u = 0.915475947

Subproblem 2
u + 2 = -2.915475947

Simplifying
u + 2 = -2.915475947

Reorder the terms:
2 + u = -2.915475947

Solving
2 + u = -2.915475947

Solving for variable 'u'.

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

Add '-2' to each side of the equation.
2 + -2 + u = -2.915475947 + -2

Combine like terms: 2 + -2 = 0
0 + u = -2.915475947 + -2
u = -2.915475947 + -2

Combine like terms: -2.915475947 + -2 = -4.915475947
u = -4.915475947

Simplifying
u = -4.915475947

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.915475947, -4.915475947}