19.5x^2+8x-6=0

Solution for 19.5x^2+8x-6=0 equation:

Simplifying
19.5x2 + 8x + -6 = 0

Reorder the terms:
-6 + 8x + 19.5x2 = 0

Solving
-6 + 8x + 19.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '19.5'.
-0.3076923077 + 0.4102564103x + x2 = 0

Move the constant term to the right:

Add '0.3076923077' to each side of the equation.
-0.3076923077 + 0.4102564103x + 0.3076923077 + x2 = 0 + 0.3076923077

Reorder the terms:
-0.3076923077 + 0.3076923077 + 0.4102564103x + x2 = 0 + 0.3076923077

Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000
0.0000000000 + 0.4102564103x + x2 = 0 + 0.3076923077
0.4102564103x + x2 = 0 + 0.3076923077

Combine like terms: 0 + 0.3076923077 = 0.3076923077
0.4102564103x + x2 = 0.3076923077

The x term is 0.4102564103x.  Take half its coefficient (0.2051282052).
Square it (0.04207758057) and add it to both sides.

Add '0.04207758057' to each side of the equation.
0.4102564103x + 0.04207758057 + x2 = 0.3076923077 + 0.04207758057

Reorder the terms:
0.04207758057 + 0.4102564103x + x2 = 0.3076923077 + 0.04207758057

Combine like terms: 0.3076923077 + 0.04207758057 = 0.34976988827
0.04207758057 + 0.4102564103x + x2 = 0.34976988827

Factor a perfect square on the left side:
(x + 0.2051282052)(x + 0.2051282052) = 0.34976988827

Calculate the square root of the right side: 0.591413466

Break this problem into two subproblems by setting 
(x + 0.2051282052) equal to 0.591413466 and -0.591413466.

Subproblem 1
x + 0.2051282052 = 0.591413466

Simplifying
x + 0.2051282052 = 0.591413466

Reorder the terms:
0.2051282052 + x = 0.591413466

Solving
0.2051282052 + x = 0.591413466

Solving for variable 'x'.

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

Add '-0.2051282052' to each side of the equation.
0.2051282052 + -0.2051282052 + x = 0.591413466 + -0.2051282052

Combine like terms: 0.2051282052 + -0.2051282052 = 0.0000000000
0.0000000000 + x = 0.591413466 + -0.2051282052
x = 0.591413466 + -0.2051282052

Combine like terms: 0.591413466 + -0.2051282052 = 0.3862852608
x = 0.3862852608

Simplifying
x = 0.3862852608

Subproblem 2
x + 0.2051282052 = -0.591413466

Simplifying
x + 0.2051282052 = -0.591413466

Reorder the terms:
0.2051282052 + x = -0.591413466

Solving
0.2051282052 + x = -0.591413466

Solving for variable 'x'.

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

Add '-0.2051282052' to each side of the equation.
0.2051282052 + -0.2051282052 + x = -0.591413466 + -0.2051282052

Combine like terms: 0.2051282052 + -0.2051282052 = 0.0000000000
0.0000000000 + x = -0.591413466 + -0.2051282052
x = -0.591413466 + -0.2051282052

Combine like terms: -0.591413466 + -0.2051282052 = -0.7965416712
x = -0.7965416712

Simplifying
x = -0.7965416712

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3862852608, -0.7965416712}