0=5x^2+10.3x-6

Solution for 0=5x^2+10.3x-6 equation:

Simplifying
0 = 5x2 + 10.3x + -6

Reorder the terms:
0 = -6 + 10.3x + 5x2

Solving
0 = -6 + 10.3x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -10.3x + -5x2 = -6 + 10.3x + 5x2 + 6 + -10.3x + -5x2

Reorder the terms:
6 + -10.3x + -5x2 = -6 + 6 + 10.3x + -10.3x + 5x2 + -5x2

Combine like terms: -6 + 6 = 0
6 + -10.3x + -5x2 = 0 + 10.3x + -10.3x + 5x2 + -5x2
6 + -10.3x + -5x2 = 10.3x + -10.3x + 5x2 + -5x2

Combine like terms: 10.3x + -10.3x = 0.0
6 + -10.3x + -5x2 = 0.0 + 5x2 + -5x2
6 + -10.3x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
6 + -10.3x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.2 + 2.06x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 2.06x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 2.06x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 2.06x + x2 = 0 + 1.2
2.06x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
2.06x + x2 = 1.2

The x term is 2.06x.  Take half its coefficient (1.03).
Square it (1.0609) and add it to both sides.

Add '1.0609' to each side of the equation.
2.06x + 1.0609 + x2 = 1.2 + 1.0609

Reorder the terms:
1.0609 + 2.06x + x2 = 1.2 + 1.0609

Combine like terms: 1.2 + 1.0609 = 2.2609
1.0609 + 2.06x + x2 = 2.2609

Factor a perfect square on the left side:
(x + 1.03)(x + 1.03) = 2.2609

Calculate the square root of the right side: 1.503628944

Break this problem into two subproblems by setting 
(x + 1.03) equal to 1.503628944 and -1.503628944.

Subproblem 1
x + 1.03 = 1.503628944

Simplifying
x + 1.03 = 1.503628944

Reorder the terms:
1.03 + x = 1.503628944

Solving
1.03 + x = 1.503628944

Solving for variable 'x'.

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

Add '-1.03' to each side of the equation.
1.03 + -1.03 + x = 1.503628944 + -1.03

Combine like terms: 1.03 + -1.03 = 0.00
0.00 + x = 1.503628944 + -1.03
x = 1.503628944 + -1.03

Combine like terms: 1.503628944 + -1.03 = 0.473628944
x = 0.473628944

Simplifying
x = 0.473628944

Subproblem 2
x + 1.03 = -1.503628944

Simplifying
x + 1.03 = -1.503628944

Reorder the terms:
1.03 + x = -1.503628944

Solving
1.03 + x = -1.503628944

Solving for variable 'x'.

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

Add '-1.03' to each side of the equation.
1.03 + -1.03 + x = -1.503628944 + -1.03

Combine like terms: 1.03 + -1.03 = 0.00
0.00 + x = -1.503628944 + -1.03
x = -1.503628944 + -1.03

Combine like terms: -1.503628944 + -1.03 = -2.533628944
x = -2.533628944

Simplifying
x = -2.533628944

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.473628944, -2.533628944}