5u^2-9u+3=0

Solution for 5u^2-9u+3=0 equation:

Simplifying
5u2 + -9u + 3 = 0

Reorder the terms:
3 + -9u + 5u2 = 0

Solving
3 + -9u + 5u2 = 0

Solving for variable 'u'.

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

Divide each side by '5'.
0.6 + -1.8u + u2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.8u + -0.6 + u2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.8u + u2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.8u + u2 = 0 + -0.6
-1.8u + u2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-1.8u + u2 = -0.6

The u term is -1.8u.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8u + 0.81 + u2 = -0.6 + 0.81

Reorder the terms:
0.81 + -1.8u + u2 = -0.6 + 0.81

Combine like terms: -0.6 + 0.81 = 0.21
0.81 + -1.8u + u2 = 0.21

Factor a perfect square on the left side:
(u + -0.9)(u + -0.9) = 0.21

Calculate the square root of the right side: 0.458257569

Break this problem into two subproblems by setting 
(u + -0.9) equal to 0.458257569 and -0.458257569.

Subproblem 1
u + -0.9 = 0.458257569

Simplifying
u + -0.9 = 0.458257569

Reorder the terms:
-0.9 + u = 0.458257569

Solving
-0.9 + u = 0.458257569

Solving for variable 'u'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + u = 0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + u = 0.458257569 + 0.9
u = 0.458257569 + 0.9

Combine like terms: 0.458257569 + 0.9 = 1.358257569
u = 1.358257569

Simplifying
u = 1.358257569

Subproblem 2
u + -0.9 = -0.458257569

Simplifying
u + -0.9 = -0.458257569

Reorder the terms:
-0.9 + u = -0.458257569

Solving
-0.9 + u = -0.458257569

Solving for variable 'u'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + u = -0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + u = -0.458257569 + 0.9
u = -0.458257569 + 0.9

Combine like terms: -0.458257569 + 0.9 = 0.441742431
u = 0.441742431

Simplifying
u = 0.441742431

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.358257569, 0.441742431}