0.5x^2-3x-20=0

Solution for 0.5x^2-3x-20=0 equation:

Simplifying
0.5x2 + -3x + -20 = 0

Reorder the terms:
-20 + -3x + 0.5x2 = 0

Solving
-20 + -3x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-40 + -6x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -6x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -6x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -6x + x2 = 0 + 40
-6x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-6x + x2 = 40

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 40 + 9

Reorder the terms:
9 + -6x + x2 = 40 + 9

Combine like terms: 40 + 9 = 49
9 + -6x + x2 = 49

Factor a perfect square on the left side:
(x + -3)(x + -3) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + -3) equal to 7 and -7.

Subproblem 1
x + -3 = 7

Simplifying
x + -3 = 7

Reorder the terms:
-3 + x = 7

Solving
-3 + x = 7

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 7 + 3

Combine like terms: -3 + 3 = 0
0 + x = 7 + 3
x = 7 + 3

Combine like terms: 7 + 3 = 10
x = 10

Simplifying
x = 10

Subproblem 2
x + -3 = -7

Simplifying
x + -3 = -7

Reorder the terms:
-3 + x = -7

Solving
-3 + x = -7

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -7 + 3

Combine like terms: -3 + 3 = 0
0 + x = -7 + 3
x = -7 + 3

Combine like terms: -7 + 3 = -4
x = -4

Simplifying
x = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, -4}