3u^2+8u+3=0

Solution for 3u^2+8u+3=0 equation:

Simplifying
3u2 + 8u + 3 = 0

Reorder the terms:
3 + 8u + 3u2 = 0

Solving
3 + 8u + 3u2 = 0

Solving for variable 'u'.

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

Divide each side by '3'.
1 + 2.666666667u + u2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.666666667u + -1 + u2 = 0 + -1

Reorder the terms:
1 + -1 + 2.666666667u + u2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.666666667u + u2 = 0 + -1
2.666666667u + u2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.666666667u + u2 = -1

The u term is 2.666666667u.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667u + 1.777777780 + u2 = -1 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667u + u2 = -1 + 1.777777780

Combine like terms: -1 + 1.777777780 = 0.77777778
1.777777780 + 2.666666667u + u2 = 0.77777778

Factor a perfect square on the left side:
(u + 1.333333334)(u + 1.333333334) = 0.77777778

Calculate the square root of the right side: 0.881917105

Break this problem into two subproblems by setting 
(u + 1.333333334) equal to 0.881917105 and -0.881917105.

Subproblem 1
u + 1.333333334 = 0.881917105

Simplifying
u + 1.333333334 = 0.881917105

Reorder the terms:
1.333333334 + u = 0.881917105

Solving
1.333333334 + u = 0.881917105

Solving for variable 'u'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + u = 0.881917105 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + u = 0.881917105 + -1.333333334
u = 0.881917105 + -1.333333334

Combine like terms: 0.881917105 + -1.333333334 = -0.451416229
u = -0.451416229

Simplifying
u = -0.451416229

Subproblem 2
u + 1.333333334 = -0.881917105

Simplifying
u + 1.333333334 = -0.881917105

Reorder the terms:
1.333333334 + u = -0.881917105

Solving
1.333333334 + u = -0.881917105

Solving for variable 'u'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + u = -0.881917105 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + u = -0.881917105 + -1.333333334
u = -0.881917105 + -1.333333334

Combine like terms: -0.881917105 + -1.333333334 = -2.215250439
u = -2.215250439

Simplifying
u = -2.215250439

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.451416229, -2.215250439}