6=0.013x^2-1.19x+28.24

Solution for 6=0.013x^2-1.19x+28.24 equation:

Simplifying
6 = 0.013x2 + -1.19x + 28.24

Reorder the terms:
6 = 28.24 + -1.19x + 0.013x2

Solving
6 = 28.24 + -1.19x + 0.013x2

Solving for variable 'x'.

Combine like terms: 6 + -28.24 = -22.24
-22.24 + 1.19x + -0.013x2 = 28.24 + -1.19x + 0.013x2 + -28.24 + 1.19x + -0.013x2

Reorder the terms:
-22.24 + 1.19x + -0.013x2 = 28.24 + -28.24 + -1.19x + 1.19x + 0.013x2 + -0.013x2

Combine like terms: 28.24 + -28.24 = 0.00
-22.24 + 1.19x + -0.013x2 = 0.00 + -1.19x + 1.19x + 0.013x2 + -0.013x2
-22.24 + 1.19x + -0.013x2 = -1.19x + 1.19x + 0.013x2 + -0.013x2

Combine like terms: -1.19x + 1.19x = 0.00
-22.24 + 1.19x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2
-22.24 + 1.19x + -0.013x2 = 0.013x2 + -0.013x2

Combine like terms: 0.013x2 + -0.013x2 = 0.000
-22.24 + 1.19x + -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'.
1710.769231 + -91.53846154x + x2 = 0

Move the constant term to the right:

Add '-1710.769231' to each side of the equation.
1710.769231 + -91.53846154x + -1710.769231 + x2 = 0 + -1710.769231

Reorder the terms:
1710.769231 + -1710.769231 + -91.53846154x + x2 = 0 + -1710.769231

Combine like terms: 1710.769231 + -1710.769231 = 0.000000
0.000000 + -91.53846154x + x2 = 0 + -1710.769231
-91.53846154x + x2 = 0 + -1710.769231

Combine like terms: 0 + -1710.769231 = -1710.769231
-91.53846154x + x2 = -1710.769231

The x term is -91.53846154x.  Take half its coefficient (-45.76923077).
Square it (2094.822485) and add it to both sides.

Add '2094.822485' to each side of the equation.
-91.53846154x + 2094.822485 + x2 = -1710.769231 + 2094.822485

Reorder the terms:
2094.822485 + -91.53846154x + x2 = -1710.769231 + 2094.822485

Combine like terms: -1710.769231 + 2094.822485 = 384.053254
2094.822485 + -91.53846154x + x2 = 384.053254

Factor a perfect square on the left side:
(x + -45.76923077)(x + -45.76923077) = 384.053254

Calculate the square root of the right side: 19.597276699

Break this problem into two subproblems by setting 
(x + -45.76923077) equal to 19.597276699 and -19.597276699.

Subproblem 1
x + -45.76923077 = 19.597276699

Simplifying
x + -45.76923077 = 19.597276699

Reorder the terms:
-45.76923077 + x = 19.597276699

Solving
-45.76923077 + x = 19.597276699

Solving for variable 'x'.

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

Add '45.76923077' to each side of the equation.
-45.76923077 + 45.76923077 + x = 19.597276699 + 45.76923077

Combine like terms: -45.76923077 + 45.76923077 = 0.00000000
0.00000000 + x = 19.597276699 + 45.76923077
x = 19.597276699 + 45.76923077

Combine like terms: 19.597276699 + 45.76923077 = 65.366507469
x = 65.366507469

Simplifying
x = 65.366507469

Subproblem 2
x + -45.76923077 = -19.597276699

Simplifying
x + -45.76923077 = -19.597276699

Reorder the terms:
-45.76923077 + x = -19.597276699

Solving
-45.76923077 + x = -19.597276699

Solving for variable 'x'.

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

Add '45.76923077' to each side of the equation.
-45.76923077 + 45.76923077 + x = -19.597276699 + 45.76923077

Combine like terms: -45.76923077 + 45.76923077 = 0.00000000
0.00000000 + x = -19.597276699 + 45.76923077
x = -19.597276699 + 45.76923077

Combine like terms: -19.597276699 + 45.76923077 = 26.171954071
x = 26.171954071

Simplifying
x = 26.171954071

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {65.366507469, 26.171954071}