3u^2+2u-9=0

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


Simplifying
3u2 + 2u + -9 = 0

Reorder the terms:
-9 + 2u + 3u2 = 0

Solving
-9 + 2u + 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'.
-3 + 0.6666666667u + u2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.6666666667u + 3 + u2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.6666666667u + u2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.6666666667u + u2 = 0 + 3
0.6666666667u + u2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.6666666667u + u2 = 3

The u term is 0.6666666667u.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667u + 0.1111111112 + u2 = 3 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667u + u2 = 3 + 0.1111111112

Combine like terms: 3 + 0.1111111112 = 3.1111111112
0.1111111112 + 0.6666666667u + u2 = 3.1111111112

Factor a perfect square on the left side:
(u + 0.3333333334)(u + 0.3333333334) = 3.1111111112

Calculate the square root of the right side: 1.763834207

Break this problem into two subproblems by setting 
(u + 0.3333333334) equal to 1.763834207 and -1.763834207.

Subproblem 1

u + 0.3333333334 = 1.763834207 Simplifying u + 0.3333333334 = 1.763834207 Reorder the terms: 0.3333333334 + u = 1.763834207 Solving 0.3333333334 + u = 1.763834207 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + u = 1.763834207 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + u = 1.763834207 + -0.3333333334 u = 1.763834207 + -0.3333333334 Combine like terms: 1.763834207 + -0.3333333334 = 1.4305008736 u = 1.4305008736 Simplifying u = 1.4305008736

Subproblem 2

u + 0.3333333334 = -1.763834207 Simplifying u + 0.3333333334 = -1.763834207 Reorder the terms: 0.3333333334 + u = -1.763834207 Solving 0.3333333334 + u = -1.763834207 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + u = -1.763834207 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + u = -1.763834207 + -0.3333333334 u = -1.763834207 + -0.3333333334 Combine like terms: -1.763834207 + -0.3333333334 = -2.0971675404 u = -2.0971675404 Simplifying u = -2.0971675404

Solution

The solution to the problem is based on the solutions from the subproblems. u = {1.4305008736, -2.0971675404}

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