20x^2=22x-12

Solution for 20x^2=22x-12 equation:

Simplifying
20x2 = 22x + -12

Reorder the terms:
20x2 = -12 + 22x

Solving
20x2 = -12 + 22x

Solving for variable 'x'.

Reorder the terms:
12 + -22x + 20x2 = -12 + 22x + 12 + -22x

Reorder the terms:
12 + -22x + 20x2 = -12 + 12 + 22x + -22x

Combine like terms: -12 + 12 = 0
12 + -22x + 20x2 = 0 + 22x + -22x
12 + -22x + 20x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
12 + -22x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -11x + 10x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -11x + 10x2)' equal to zero and attempt to solve:

Simplifying
6 + -11x + 10x2 = 0

Solving
6 + -11x + 10x2 = 0

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

Divide each side by '10'.
0.6 + -1.1x + x2 = 0.0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.1x + -0.6 + x2 = 0.0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.1x + x2 = 0.0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.1x + x2 = 0.0 + -0.6
-1.1x + x2 = 0.0 + -0.6

Combine like terms: 0.0 + -0.6 = -0.6
-1.1x + x2 = -0.6

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = -0.6 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = -0.6 + 0.3025

Combine like terms: -0.6 + 0.3025 = -0.2975
0.3025 + -1.1x + x2 = -0.2975

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = -0.2975

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.