-0.09x^2+x+1.20=0

Solution for -0.09x^2+x+1.20=0 equation:

Simplifying
-0.09x2 + x + 1.20 = 0

Reorder the terms:
1.20 + x + -0.09x2 = 0

Solving
1.20 + x + -0.09x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.09 the coefficient of the squared term: 

Divide each side by '-0.09'.
-13.33333333 + -11.11111111x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -11.11111111x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -11.11111111x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -11.11111111x + x2 = 0 + 13.33333333
-11.11111111x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-11.11111111x + x2 = 13.33333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-11.11111111x + 0.25 + x2 = 13.33333333 + 0.25

Reorder the terms:
0.25 + -11.11111111x + x2 = 13.33333333 + 0.25

Combine like terms: 13.33333333 + 0.25 = 13.58333333
0.25 + -11.11111111x + x2 = 13.58333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.58333333

Calculate the square root of the right side: 3.685557397

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.685557397 and -3.685557397.

Subproblem 1
x + 0.5 = 3.685557397

Simplifying
x + 0.5 = 3.685557397

Reorder the terms:
0.5 + x = 3.685557397

Solving
0.5 + x = 3.685557397

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.685557397 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.685557397 + -0.5
x = 3.685557397 + -0.5

Combine like terms: 3.685557397 + -0.5 = 3.185557397
x = 3.185557397

Simplifying
x = 3.185557397

Subproblem 2
x + 0.5 = -3.685557397

Simplifying
x + 0.5 = -3.685557397

Reorder the terms:
0.5 + x = -3.685557397

Solving
0.5 + x = -3.685557397

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.685557397 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.685557397 + -0.5
x = -3.685557397 + -0.5

Combine like terms: -3.685557397 + -0.5 = -4.185557397
x = -4.185557397

Simplifying
x = -4.185557397

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.185557397, -4.185557397}