10.1=0.8087x^2-6.4654x+20.792

Solution for 10.1=0.8087x^2-6.4654x+20.792 equation:

Simplifying
10.1 = 0.8087x2 + -6.4654x + 20.792

Reorder the terms:
10.1 = 20.792 + -6.4654x + 0.8087x2

Solving
10.1 = 20.792 + -6.4654x + 0.8087x2

Solving for variable 'x'.

Combine like terms: 10.1 + -20.792 = -10.692
-10.692 + 6.4654x + -0.8087x2 = 20.792 + -6.4654x + 0.8087x2 + -20.792 + 6.4654x + -0.8087x2

Reorder the terms:
-10.692 + 6.4654x + -0.8087x2 = 20.792 + -20.792 + -6.4654x + 6.4654x + 0.8087x2 + -0.8087x2

Combine like terms: 20.792 + -20.792 = 0.000
-10.692 + 6.4654x + -0.8087x2 = 0.000 + -6.4654x + 6.4654x + 0.8087x2 + -0.8087x2
-10.692 + 6.4654x + -0.8087x2 = -6.4654x + 6.4654x + 0.8087x2 + -0.8087x2

Combine like terms: -6.4654x + 6.4654x = 0.0000
-10.692 + 6.4654x + -0.8087x2 = 0.0000 + 0.8087x2 + -0.8087x2
-10.692 + 6.4654x + -0.8087x2 = 0.8087x2 + -0.8087x2

Combine like terms: 0.8087x2 + -0.8087x2 = 0.0000
-10.692 + 6.4654x + -0.8087x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.8087 the coefficient of the squared term: 

Divide each side by '-0.8087'.
13.22121924 + -7.99480648x + x2 = 0

Move the constant term to the right:

Add '-13.22121924' to each side of the equation.
13.22121924 + -7.99480648x + -13.22121924 + x2 = 0 + -13.22121924

Reorder the terms:
13.22121924 + -13.22121924 + -7.99480648x + x2 = 0 + -13.22121924

Combine like terms: 13.22121924 + -13.22121924 = 0.00000000
0.00000000 + -7.99480648x + x2 = 0 + -13.22121924
-7.99480648x + x2 = 0 + -13.22121924

Combine like terms: 0 + -13.22121924 = -13.22121924
-7.99480648x + x2 = -13.22121924

The x term is -7.99480648x.  Take half its coefficient (-3.99740324).
Square it (15.97923266) and add it to both sides.

Add '15.97923266' to each side of the equation.
-7.99480648x + 15.97923266 + x2 = -13.22121924 + 15.97923266

Reorder the terms:
15.97923266 + -7.99480648x + x2 = -13.22121924 + 15.97923266

Combine like terms: -13.22121924 + 15.97923266 = 2.75801342
15.97923266 + -7.99480648x + x2 = 2.75801342

Factor a perfect square on the left side:
(x + -3.99740324)(x + -3.99740324) = 2.75801342

Calculate the square root of the right side: 1.660726775

Break this problem into two subproblems by setting 
(x + -3.99740324) equal to 1.660726775 and -1.660726775.

Subproblem 1
x + -3.99740324 = 1.660726775

Simplifying
x + -3.99740324 = 1.660726775

Reorder the terms:
-3.99740324 + x = 1.660726775

Solving
-3.99740324 + x = 1.660726775

Solving for variable 'x'.

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

Add '3.99740324' to each side of the equation.
-3.99740324 + 3.99740324 + x = 1.660726775 + 3.99740324

Combine like terms: -3.99740324 + 3.99740324 = 0.00000000
0.00000000 + x = 1.660726775 + 3.99740324
x = 1.660726775 + 3.99740324

Combine like terms: 1.660726775 + 3.99740324 = 5.658130015
x = 5.658130015

Simplifying
x = 5.658130015

Subproblem 2
x + -3.99740324 = -1.660726775

Simplifying
x + -3.99740324 = -1.660726775

Reorder the terms:
-3.99740324 + x = -1.660726775

Solving
-3.99740324 + x = -1.660726775

Solving for variable 'x'.

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

Add '3.99740324' to each side of the equation.
-3.99740324 + 3.99740324 + x = -1.660726775 + 3.99740324

Combine like terms: -3.99740324 + 3.99740324 = 0.00000000
0.00000000 + x = -1.660726775 + 3.99740324
x = -1.660726775 + 3.99740324

Combine like terms: -1.660726775 + 3.99740324 = 2.336676465
x = 2.336676465

Simplifying
x = 2.336676465

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.658130015, 2.336676465}