13.15=0.192x^2-2.33x+19.5

Solution for 13.15=0.192x^2-2.33x+19.5 equation:

Simplifying
13.15 = 0.192x2 + -2.33x + 19.5

Reorder the terms:
13.15 = 19.5 + -2.33x + 0.192x2

Solving
13.15 = 19.5 + -2.33x + 0.192x2

Solving for variable 'x'.

Combine like terms: 13.15 + -19.5 = -6.35
-6.35 + 2.33x + -0.192x2 = 19.5 + -2.33x + 0.192x2 + -19.5 + 2.33x + -0.192x2

Reorder the terms:
-6.35 + 2.33x + -0.192x2 = 19.5 + -19.5 + -2.33x + 2.33x + 0.192x2 + -0.192x2

Combine like terms: 19.5 + -19.5 = 0.0
-6.35 + 2.33x + -0.192x2 = 0.0 + -2.33x + 2.33x + 0.192x2 + -0.192x2
-6.35 + 2.33x + -0.192x2 = -2.33x + 2.33x + 0.192x2 + -0.192x2

Combine like terms: -2.33x + 2.33x = 0.00
-6.35 + 2.33x + -0.192x2 = 0.00 + 0.192x2 + -0.192x2
-6.35 + 2.33x + -0.192x2 = 0.192x2 + -0.192x2

Combine like terms: 0.192x2 + -0.192x2 = 0.000
-6.35 + 2.33x + -0.192x2 = 0.000

Begin completing the square.  Divide all terms by
-0.192 the coefficient of the squared term: 

Divide each side by '-0.192'.
33.07291667 + -12.13541667x + x2 = 0

Move the constant term to the right:

Add '-33.07291667' to each side of the equation.
33.07291667 + -12.13541667x + -33.07291667 + x2 = 0 + -33.07291667

Reorder the terms:
33.07291667 + -33.07291667 + -12.13541667x + x2 = 0 + -33.07291667

Combine like terms: 33.07291667 + -33.07291667 = 0.00000000
0.00000000 + -12.13541667x + x2 = 0 + -33.07291667
-12.13541667x + x2 = 0 + -33.07291667

Combine like terms: 0 + -33.07291667 = -33.07291667
-12.13541667x + x2 = -33.07291667

The x term is -12.13541667x.  Take half its coefficient (-6.067708335).
Square it (36.81708444) and add it to both sides.

Add '36.81708444' to each side of the equation.
-12.13541667x + 36.81708444 + x2 = -33.07291667 + 36.81708444

Reorder the terms:
36.81708444 + -12.13541667x + x2 = -33.07291667 + 36.81708444

Combine like terms: -33.07291667 + 36.81708444 = 3.74416777
36.81708444 + -12.13541667x + x2 = 3.74416777

Factor a perfect square on the left side:
(x + -6.067708335)(x + -6.067708335) = 3.74416777

Calculate the square root of the right side: 1.934985212

Break this problem into two subproblems by setting 
(x + -6.067708335) equal to 1.934985212 and -1.934985212.

Subproblem 1
x + -6.067708335 = 1.934985212

Simplifying
x + -6.067708335 = 1.934985212

Reorder the terms:
-6.067708335 + x = 1.934985212

Solving
-6.067708335 + x = 1.934985212

Solving for variable 'x'.

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

Add '6.067708335' to each side of the equation.
-6.067708335 + 6.067708335 + x = 1.934985212 + 6.067708335

Combine like terms: -6.067708335 + 6.067708335 = 0.000000000
0.000000000 + x = 1.934985212 + 6.067708335
x = 1.934985212 + 6.067708335

Combine like terms: 1.934985212 + 6.067708335 = 8.002693547
x = 8.002693547

Simplifying
x = 8.002693547

Subproblem 2
x + -6.067708335 = -1.934985212

Simplifying
x + -6.067708335 = -1.934985212

Reorder the terms:
-6.067708335 + x = -1.934985212

Solving
-6.067708335 + x = -1.934985212

Solving for variable 'x'.

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

Add '6.067708335' to each side of the equation.
-6.067708335 + 6.067708335 + x = -1.934985212 + 6.067708335

Combine like terms: -6.067708335 + 6.067708335 = 0.000000000
0.000000000 + x = -1.934985212 + 6.067708335
x = -1.934985212 + 6.067708335

Combine like terms: -1.934985212 + 6.067708335 = 4.132723123
x = 4.132723123

Simplifying
x = 4.132723123

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.002693547, 4.132723123}