12u^2+7u-3=0

Solution for 12u^2+7u-3=0 equation:

Simplifying
12u2 + 7u + -3 = 0

Reorder the terms:
-3 + 7u + 12u2 = 0

Solving
-3 + 7u + 12u2 = 0

Solving for variable 'u'.

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

Divide each side by '12'.
-0.25 + 0.5833333333u + u2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.5833333333u + 0.25 + u2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.5833333333u + u2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.5833333333u + u2 = 0 + 0.25
0.5833333333u + u2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.5833333333u + u2 = 0.25

The u term is 0.5833333333u.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333u + 0.08506944446 + u2 = 0.25 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333u + u2 = 0.25 + 0.08506944446

Combine like terms: 0.25 + 0.08506944446 = 0.33506944446
0.08506944446 + 0.5833333333u + u2 = 0.33506944446

Factor a perfect square on the left side:
(u + 0.2916666667)(u + 0.2916666667) = 0.33506944446

Calculate the square root of the right side: 0.578851833

Break this problem into two subproblems by setting 
(u + 0.2916666667) equal to 0.578851833 and -0.578851833.

Subproblem 1
u + 0.2916666667 = 0.578851833

Simplifying
u + 0.2916666667 = 0.578851833

Reorder the terms:
0.2916666667 + u = 0.578851833

Solving
0.2916666667 + u = 0.578851833

Solving for variable 'u'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + u = 0.578851833 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + u = 0.578851833 + -0.2916666667
u = 0.578851833 + -0.2916666667

Combine like terms: 0.578851833 + -0.2916666667 = 0.2871851663
u = 0.2871851663

Simplifying
u = 0.2871851663

Subproblem 2
u + 0.2916666667 = -0.578851833

Simplifying
u + 0.2916666667 = -0.578851833

Reorder the terms:
0.2916666667 + u = -0.578851833

Solving
0.2916666667 + u = -0.578851833

Solving for variable 'u'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + u = -0.578851833 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + u = -0.578851833 + -0.2916666667
u = -0.578851833 + -0.2916666667

Combine like terms: -0.578851833 + -0.2916666667 = -0.8705184997
u = -0.8705184997

Simplifying
u = -0.8705184997

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.2871851663, -0.8705184997}