3u^2=24u-3

Solution for 3u^2=24u-3 equation:

Simplifying
3u2 = 24u + -3

Reorder the terms:
3u2 = -3 + 24u

Solving
3u2 = -3 + 24u

Solving for variable 'u'.

Reorder the terms:
3 + -24u + 3u2 = -3 + 24u + 3 + -24u

Reorder the terms:
3 + -24u + 3u2 = -3 + 3 + 24u + -24u

Combine like terms: -3 + 3 = 0
3 + -24u + 3u2 = 0 + 24u + -24u
3 + -24u + 3u2 = 24u + -24u

Combine like terms: 24u + -24u = 0
3 + -24u + 3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -8u + u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -8u + u2)' equal to zero and attempt to solve:

Simplifying
1 + -8u + u2 = 0

Solving
1 + -8u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -8u + -1 + u2 = 0 + -1

Reorder the terms:
1 + -1 + -8u + u2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8u + u2 = 0 + -1
-8u + u2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8u + u2 = -1

The u term is -8u.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8u + 16 + u2 = -1 + 16

Reorder the terms:
16 + -8u + u2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + -8u + u2 = 15

Factor a perfect square on the left side:
(u + -4)(u + -4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(u + -4) equal to 3.872983346 and -3.872983346.

Subproblem 1
u + -4 = 3.872983346

Simplifying
u + -4 = 3.872983346

Reorder the terms:
-4 + u = 3.872983346

Solving
-4 + u = 3.872983346

Solving for variable 'u'.

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

Add '4' to each side of the equation.
-4 + 4 + u = 3.872983346 + 4

Combine like terms: -4 + 4 = 0
0 + u = 3.872983346 + 4
u = 3.872983346 + 4

Combine like terms: 3.872983346 + 4 = 7.872983346
u = 7.872983346

Simplifying
u = 7.872983346

Subproblem 2
u + -4 = -3.872983346

Simplifying
u + -4 = -3.872983346

Reorder the terms:
-4 + u = -3.872983346

Solving
-4 + u = -3.872983346

Solving for variable 'u'.

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

Add '4' to each side of the equation.
-4 + 4 + u = -3.872983346 + 4

Combine like terms: -4 + 4 = 0
0 + u = -3.872983346 + 4
u = -3.872983346 + 4

Combine like terms: -3.872983346 + 4 = 0.127016654
u = 0.127016654

Simplifying
u = 0.127016654

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.872983346, 0.127016654}
Solution
u = {7.872983346, 0.127016654}