-0.05x^2+1.2x-4=0

Solution for -0.05x^2+1.2x-4=0 equation:

Simplifying
-0.05x2 + 1.2x + -4 = 0

Reorder the terms:
-4 + 1.2x + -0.05x2 = 0

Solving
-4 + 1.2x + -0.05x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
80 + -24x + x2 = 0

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + -24x + -80 + x2 = 0 + -80

Reorder the terms:
80 + -80 + -24x + x2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -24x + x2 = 0 + -80
-24x + x2 = 0 + -80

Combine like terms: 0 + -80 = -80
-24x + x2 = -80

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -80 + 144

Reorder the terms:
144 + -24x + x2 = -80 + 144

Combine like terms: -80 + 144 = 64
144 + -24x + x2 = 64

Factor a perfect square on the left side:
(x + -12)(x + -12) = 64

Calculate the square root of the right side: 8

Break this problem into two subproblems by setting 
(x + -12) equal to 8 and -8.

Subproblem 1
x + -12 = 8

Simplifying
x + -12 = 8

Reorder the terms:
-12 + x = 8

Solving
-12 + x = 8

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 8 + 12

Combine like terms: -12 + 12 = 0
0 + x = 8 + 12
x = 8 + 12

Combine like terms: 8 + 12 = 20
x = 20

Simplifying
x = 20

Subproblem 2
x + -12 = -8

Simplifying
x + -12 = -8

Reorder the terms:
-12 + x = -8

Solving
-12 + x = -8

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -8 + 12

Combine like terms: -12 + 12 = 0
0 + x = -8 + 12
x = -8 + 12

Combine like terms: -8 + 12 = 4
x = 4

Simplifying
x = 4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20, 4}