(.3x^2)-1.1x-2=(-.4x^2)+.5x+8.3

Solution for (.3x^2)-1.1x-2=(-.4x^2)+.5x+8.3 equation:

Simplifying
(0.3x2) + -1.1x + -2 = (-0.4x2) + 0.5x + 8.3

Reorder the terms:
-2 + -1.1x + (0.3x2) = (-0.4x2) + 0.5x + 8.3

Reorder the terms:
-2 + -1.1x + (0.3x2) = 8.3 + 0.5x + (-0.4x2)

Solving
-2 + -1.1x + (0.3x2) = 8.3 + 0.5x + (-0.4x2)

Solving for variable 'x'.

Reorder the terms:
-2 + -8.3 + -1.1x + -0.5x + (0.3x2) + (0.4x2) = 8.3 + 0.5x + (-0.4x2) + -8.3 + -0.5x + (0.4x2)

Combine like terms: -2 + -8.3 = -10.3
-10.3 + -1.1x + -0.5x + (0.3x2) + (0.4x2) = 8.3 + 0.5x + (-0.4x2) + -8.3 + -0.5x + (0.4x2)

Combine like terms: -1.1x + -0.5x = -1.6x
-10.3 + -1.6x + (0.3x2) + (0.4x2) = 8.3 + 0.5x + (-0.4x2) + -8.3 + -0.5x + (0.4x2)

Combine like terms: (0.3x2) + (0.4x2) = 0.7x2
-10.3 + -1.6x + 0.7x2 = 8.3 + 0.5x + (-0.4x2) + -8.3 + -0.5x + (0.4x2)

Reorder the terms:
-10.3 + -1.6x + 0.7x2 = 8.3 + -8.3 + 0.5x + -0.5x + (-0.4x2) + (0.4x2)

Combine like terms: 8.3 + -8.3 = 0.0
-10.3 + -1.6x + 0.7x2 = 0.0 + 0.5x + -0.5x + (-0.4x2) + (0.4x2)
-10.3 + -1.6x + 0.7x2 = 0.5x + -0.5x + (-0.4x2) + (0.4x2)

Combine like terms: 0.5x + -0.5x = 0.0
-10.3 + -1.6x + 0.7x2 = 0.0 + (-0.4x2) + (0.4x2)
-10.3 + -1.6x + 0.7x2 = (-0.4x2) + (0.4x2)

Combine like terms: (-0.4x2) + (0.4x2) = 0.0
-10.3 + -1.6x + 0.7x2 = 0.0

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

Divide each side by '0.7'.
-14.71428571 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '14.71428571' to each side of the equation.
-14.71428571 + -2.285714286x + 14.71428571 + x2 = 0 + 14.71428571

Reorder the terms:
-14.71428571 + 14.71428571 + -2.285714286x + x2 = 0 + 14.71428571

Combine like terms: -14.71428571 + 14.71428571 = 0.00000000
0.00000000 + -2.285714286x + x2 = 0 + 14.71428571
-2.285714286x + x2 = 0 + 14.71428571

Combine like terms: 0 + 14.71428571 = 14.71428571
-2.285714286x + x2 = 14.71428571

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = 14.71428571 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = 14.71428571 + 1.306122449

Combine like terms: 14.71428571 + 1.306122449 = 16.020408159
1.306122449 + -2.285714286x + x2 = 16.020408159

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 16.020408159

Calculate the square root of the right side: 4.002550207

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 4.002550207 and -4.002550207.

Subproblem 1
x + -1.142857143 = 4.002550207

Simplifying
x + -1.142857143 = 4.002550207

Reorder the terms:
-1.142857143 + x = 4.002550207

Solving
-1.142857143 + x = 4.002550207

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = 4.002550207 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = 4.002550207 + 1.142857143
x = 4.002550207 + 1.142857143

Combine like terms: 4.002550207 + 1.142857143 = 5.14540735
x = 5.14540735

Simplifying
x = 5.14540735

Subproblem 2
x + -1.142857143 = -4.002550207

Simplifying
x + -1.142857143 = -4.002550207

Reorder the terms:
-1.142857143 + x = -4.002550207

Solving
-1.142857143 + x = -4.002550207

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = -4.002550207 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = -4.002550207 + 1.142857143
x = -4.002550207 + 1.142857143

Combine like terms: -4.002550207 + 1.142857143 = -2.859693064
x = -2.859693064

Simplifying
x = -2.859693064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.14540735, -2.859693064}