6=5x^2-9x+12

Solution for 6=5x^2-9x+12 equation:

Simplifying
6 = 5x2 + -9x + 12

Reorder the terms:
6 = 12 + -9x + 5x2

Solving
6 = 12 + -9x + 5x2

Solving for variable 'x'.

Combine like terms: 6 + -12 = -6
-6 + 9x + -5x2 = 12 + -9x + 5x2 + -12 + 9x + -5x2

Reorder the terms:
-6 + 9x + -5x2 = 12 + -12 + -9x + 9x + 5x2 + -5x2

Combine like terms: 12 + -12 = 0
-6 + 9x + -5x2 = 0 + -9x + 9x + 5x2 + -5x2
-6 + 9x + -5x2 = -9x + 9x + 5x2 + -5x2

Combine like terms: -9x + 9x = 0
-6 + 9x + -5x2 = 0 + 5x2 + -5x2
-6 + 9x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6 + 9x + -5x2 = 0

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

Divide each side by '-5'.
1.2 + -1.8x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -1.8x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -1.8x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -1.8x + x2 = 0 + -1.2
-1.8x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-1.8x + x2 = -1.2

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = -1.2 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -1.2 + 0.81

Combine like terms: -1.2 + 0.81 = -0.39
0.81 + -1.8x + x2 = -0.39

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = -0.39

Can't calculate square root of the right side.

The solution to this equation could not be determined.