4.82x^2-11.13x+3.84=0

Solution for 4.82x^2-11.13x+3.84=0 equation:

Simplifying
4.82x2 + -11.13x + 3.84 = 0

Reorder the terms:
3.84 + -11.13x + 4.82x2 = 0

Solving
3.84 + -11.13x + 4.82x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.82'.
0.7966804979 + -2.309128631x + x2 = 0

Move the constant term to the right:

Add '-0.7966804979' to each side of the equation.
0.7966804979 + -2.309128631x + -0.7966804979 + x2 = 0 + -0.7966804979

Reorder the terms:
0.7966804979 + -0.7966804979 + -2.309128631x + x2 = 0 + -0.7966804979

Combine like terms: 0.7966804979 + -0.7966804979 = 0.0000000000
0.0000000000 + -2.309128631x + x2 = 0 + -0.7966804979
-2.309128631x + x2 = 0 + -0.7966804979

Combine like terms: 0 + -0.7966804979 = -0.7966804979
-2.309128631x + x2 = -0.7966804979

The x term is -2.309128631x.  Take half its coefficient (-1.154564316).
Square it (1.333018760) and add it to both sides.

Add '1.333018760' to each side of the equation.
-2.309128631x + 1.333018760 + x2 = -0.7966804979 + 1.333018760

Reorder the terms:
1.333018760 + -2.309128631x + x2 = -0.7966804979 + 1.333018760

Combine like terms: -0.7966804979 + 1.333018760 = 0.5363382621
1.333018760 + -2.309128631x + x2 = 0.5363382621

Factor a perfect square on the left side:
(x + -1.154564316)(x + -1.154564316) = 0.5363382621

Calculate the square root of the right side: 0.732351188

Break this problem into two subproblems by setting 
(x + -1.154564316) equal to 0.732351188 and -0.732351188.

Subproblem 1
x + -1.154564316 = 0.732351188

Simplifying
x + -1.154564316 = 0.732351188

Reorder the terms:
-1.154564316 + x = 0.732351188

Solving
-1.154564316 + x = 0.732351188

Solving for variable 'x'.

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

Add '1.154564316' to each side of the equation.
-1.154564316 + 1.154564316 + x = 0.732351188 + 1.154564316

Combine like terms: -1.154564316 + 1.154564316 = 0.000000000
0.000000000 + x = 0.732351188 + 1.154564316
x = 0.732351188 + 1.154564316

Combine like terms: 0.732351188 + 1.154564316 = 1.886915504
x = 1.886915504

Simplifying
x = 1.886915504

Subproblem 2
x + -1.154564316 = -0.732351188

Simplifying
x + -1.154564316 = -0.732351188

Reorder the terms:
-1.154564316 + x = -0.732351188

Solving
-1.154564316 + x = -0.732351188

Solving for variable 'x'.

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

Add '1.154564316' to each side of the equation.
-1.154564316 + 1.154564316 + x = -0.732351188 + 1.154564316

Combine like terms: -1.154564316 + 1.154564316 = 0.000000000
0.000000000 + x = -0.732351188 + 1.154564316
x = -0.732351188 + 1.154564316

Combine like terms: -0.732351188 + 1.154564316 = 0.422213128
x = 0.422213128

Simplifying
x = 0.422213128

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.886915504, 0.422213128}