9n+4.76=3n^2

Solution for 9n+4.76=3n^2 equation:

Simplifying
9n + 4.76 = 3n2

Reorder the terms:
4.76 + 9n = 3n2

Solving
4.76 + 9n = 3n2

Solving for variable 'n'.

Combine like terms: 3n2 + -3n2 = 0
4.76 + 9n + -3n2 = 0

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

Divide each side by '-3'.
-1.586666667 + -3n + n2 = 0

Move the constant term to the right:

Add '1.586666667' to each side of the equation.
-1.586666667 + -3n + 1.586666667 + n2 = 0 + 1.586666667

Reorder the terms:
-1.586666667 + 1.586666667 + -3n + n2 = 0 + 1.586666667

Combine like terms: -1.586666667 + 1.586666667 = 0.000000000
0.000000000 + -3n + n2 = 0 + 1.586666667
-3n + n2 = 0 + 1.586666667

Combine like terms: 0 + 1.586666667 = 1.586666667
-3n + n2 = 1.586666667

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 1.586666667 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 1.586666667 + 2.25

Combine like terms: 1.586666667 + 2.25 = 3.836666667
2.25 + -3n + n2 = 3.836666667

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 3.836666667

Calculate the square root of the right side: 1.958741092

Break this problem into two subproblems by setting 
(n + -1.5) equal to 1.958741092 and -1.958741092.

Subproblem 1
n + -1.5 = 1.958741092

Simplifying
n + -1.5 = 1.958741092

Reorder the terms:
-1.5 + n = 1.958741092

Solving
-1.5 + n = 1.958741092

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 1.958741092 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 1.958741092 + 1.5
n = 1.958741092 + 1.5

Combine like terms: 1.958741092 + 1.5 = 3.458741092
n = 3.458741092

Simplifying
n = 3.458741092

Subproblem 2
n + -1.5 = -1.958741092

Simplifying
n + -1.5 = -1.958741092

Reorder the terms:
-1.5 + n = -1.958741092

Solving
-1.5 + n = -1.958741092

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -1.958741092 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -1.958741092 + 1.5
n = -1.958741092 + 1.5

Combine like terms: -1.958741092 + 1.5 = -0.458741092
n = -0.458741092

Simplifying
n = -0.458741092

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.458741092, -0.458741092}