3=0.013x^2-1.18x+28.23

Solution for 3=0.013x^2-1.18x+28.23 equation:

Simplifying
3 = 0.013x2 + -1.18x + 28.23

Reorder the terms:
3 = 28.23 + -1.18x + 0.013x2

Solving
3 = 28.23 + -1.18x + 0.013x2

Solving for variable 'x'.

Combine like terms: 3 + -28.23 = -25.23
-25.23 + 1.18x + -0.013x2 = 28.23 + -1.18x + 0.013x2 + -28.23 + 1.18x + -0.013x2

Reorder the terms:
-25.23 + 1.18x + -0.013x2 = 28.23 + -28.23 + -1.18x + 1.18x + 0.013x2 + -0.013x2

Combine like terms: 28.23 + -28.23 = 0.00
-25.23 + 1.18x + -0.013x2 = 0.00 + -1.18x + 1.18x + 0.013x2 + -0.013x2
-25.23 + 1.18x + -0.013x2 = -1.18x + 1.18x + 0.013x2 + -0.013x2

Combine like terms: -1.18x + 1.18x = 0.00
-25.23 + 1.18x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2
-25.23 + 1.18x + -0.013x2 = 0.013x2 + -0.013x2

Combine like terms: 0.013x2 + -0.013x2 = 0.000
-25.23 + 1.18x + -0.013x2 = 0.000

Begin completing the square.  Divide all terms by
-0.013 the coefficient of the squared term: 

Divide each side by '-0.013'.
1940.769231 + -90.76923077x + x2 = 0

Move the constant term to the right:

Add '-1940.769231' to each side of the equation.
1940.769231 + -90.76923077x + -1940.769231 + x2 = 0 + -1940.769231

Reorder the terms:
1940.769231 + -1940.769231 + -90.76923077x + x2 = 0 + -1940.769231

Combine like terms: 1940.769231 + -1940.769231 = 0.000000
0.000000 + -90.76923077x + x2 = 0 + -1940.769231
-90.76923077x + x2 = 0 + -1940.769231

Combine like terms: 0 + -1940.769231 = -1940.769231
-90.76923077x + x2 = -1940.769231

The x term is -90.76923077x.  Take half its coefficient (-45.38461539).
Square it (2059.763314) and add it to both sides.

Add '2059.763314' to each side of the equation.
-90.76923077x + 2059.763314 + x2 = -1940.769231 + 2059.763314

Reorder the terms:
2059.763314 + -90.76923077x + x2 = -1940.769231 + 2059.763314

Combine like terms: -1940.769231 + 2059.763314 = 118.994083
2059.763314 + -90.76923077x + x2 = 118.994083

Factor a perfect square on the left side:
(x + -45.38461539)(x + -45.38461539) = 118.994083

Calculate the square root of the right side: 10.908440906

Break this problem into two subproblems by setting 
(x + -45.38461539) equal to 10.908440906 and -10.908440906.

Subproblem 1
x + -45.38461539 = 10.908440906

Simplifying
x + -45.38461539 = 10.908440906

Reorder the terms:
-45.38461539 + x = 10.908440906

Solving
-45.38461539 + x = 10.908440906

Solving for variable 'x'.

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

Add '45.38461539' to each side of the equation.
-45.38461539 + 45.38461539 + x = 10.908440906 + 45.38461539

Combine like terms: -45.38461539 + 45.38461539 = 0.00000000
0.00000000 + x = 10.908440906 + 45.38461539
x = 10.908440906 + 45.38461539

Combine like terms: 10.908440906 + 45.38461539 = 56.293056296
x = 56.293056296

Simplifying
x = 56.293056296

Subproblem 2
x + -45.38461539 = -10.908440906

Simplifying
x + -45.38461539 = -10.908440906

Reorder the terms:
-45.38461539 + x = -10.908440906

Solving
-45.38461539 + x = -10.908440906

Solving for variable 'x'.

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

Add '45.38461539' to each side of the equation.
-45.38461539 + 45.38461539 + x = -10.908440906 + 45.38461539

Combine like terms: -45.38461539 + 45.38461539 = 0.00000000
0.00000000 + x = -10.908440906 + 45.38461539
x = -10.908440906 + 45.38461539

Combine like terms: -10.908440906 + 45.38461539 = 34.476174484
x = 34.476174484

Simplifying
x = 34.476174484

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.293056296, 34.476174484}