(.1x^2)-1.5x-4=(-.3x^2)+.7x+8.3

Solution for (.1x^2)-1.5x-4=(-.3x^2)+.7x+8.3 equation:

Simplifying
(0.1x2) + -1.5x + -4 = (-0.3x2) + 0.7x + 8.3

Reorder the terms:
-4 + -1.5x + (0.1x2) = (-0.3x2) + 0.7x + 8.3

Reorder the terms:
-4 + -1.5x + (0.1x2) = 8.3 + 0.7x + (-0.3x2)

Solving
-4 + -1.5x + (0.1x2) = 8.3 + 0.7x + (-0.3x2)

Solving for variable 'x'.

Reorder the terms:
-4 + -8.3 + -1.5x + -0.7x + (0.1x2) + (0.3x2) = 8.3 + 0.7x + (-0.3x2) + -8.3 + -0.7x + (0.3x2)

Combine like terms: -4 + -8.3 = -12.3
-12.3 + -1.5x + -0.7x + (0.1x2) + (0.3x2) = 8.3 + 0.7x + (-0.3x2) + -8.3 + -0.7x + (0.3x2)

Combine like terms: -1.5x + -0.7x = -2.2x
-12.3 + -2.2x + (0.1x2) + (0.3x2) = 8.3 + 0.7x + (-0.3x2) + -8.3 + -0.7x + (0.3x2)

Combine like terms: (0.1x2) + (0.3x2) = 0.4x2
-12.3 + -2.2x + 0.4x2 = 8.3 + 0.7x + (-0.3x2) + -8.3 + -0.7x + (0.3x2)

Reorder the terms:
-12.3 + -2.2x + 0.4x2 = 8.3 + -8.3 + 0.7x + -0.7x + (-0.3x2) + (0.3x2)

Combine like terms: 8.3 + -8.3 = 0.0
-12.3 + -2.2x + 0.4x2 = 0.0 + 0.7x + -0.7x + (-0.3x2) + (0.3x2)
-12.3 + -2.2x + 0.4x2 = 0.7x + -0.7x + (-0.3x2) + (0.3x2)

Combine like terms: 0.7x + -0.7x = 0.0
-12.3 + -2.2x + 0.4x2 = 0.0 + (-0.3x2) + (0.3x2)
-12.3 + -2.2x + 0.4x2 = (-0.3x2) + (0.3x2)

Combine like terms: (-0.3x2) + (0.3x2) = 0.0
-12.3 + -2.2x + 0.4x2 = 0.0

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

Divide each side by '0.4'.
-30.75 + -5.5x + x2 = 0

Move the constant term to the right:

Add '30.75' to each side of the equation.
-30.75 + -5.5x + 30.75 + x2 = 0 + 30.75

Reorder the terms:
-30.75 + 30.75 + -5.5x + x2 = 0 + 30.75

Combine like terms: -30.75 + 30.75 = 0.00
0.00 + -5.5x + x2 = 0 + 30.75
-5.5x + x2 = 0 + 30.75

Combine like terms: 0 + 30.75 = 30.75
-5.5x + x2 = 30.75

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 30.75 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 30.75 + 7.5625

Combine like terms: 30.75 + 7.5625 = 38.3125
7.5625 + -5.5x + x2 = 38.3125

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 38.3125

Calculate the square root of the right side: 6.189709202

Break this problem into two subproblems by setting 
(x + -2.75) equal to 6.189709202 and -6.189709202.

Subproblem 1
x + -2.75 = 6.189709202

Simplifying
x + -2.75 = 6.189709202

Reorder the terms:
-2.75 + x = 6.189709202

Solving
-2.75 + x = 6.189709202

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 6.189709202 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 6.189709202 + 2.75
x = 6.189709202 + 2.75

Combine like terms: 6.189709202 + 2.75 = 8.939709202
x = 8.939709202

Simplifying
x = 8.939709202

Subproblem 2
x + -2.75 = -6.189709202

Simplifying
x + -2.75 = -6.189709202

Reorder the terms:
-2.75 + x = -6.189709202

Solving
-2.75 + x = -6.189709202

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -6.189709202 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -6.189709202 + 2.75
x = -6.189709202 + 2.75

Combine like terms: -6.189709202 + 2.75 = -3.439709202
x = -3.439709202

Simplifying
x = -3.439709202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.939709202, -3.439709202}