0=5x^2-3x+6

Solution for 0=5x^2-3x+6 equation:

Simplifying
0 = 5x2 + -3x + 6

Reorder the terms:
0 = 6 + -3x + 5x2

Solving
0 = 6 + -3x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 3x + -5x2 = 6 + -3x + 5x2 + -6 + 3x + -5x2

Reorder the terms:
-6 + 3x + -5x2 = 6 + -6 + -3x + 3x + 5x2 + -5x2

Combine like terms: 6 + -6 = 0
-6 + 3x + -5x2 = 0 + -3x + 3x + 5x2 + -5x2
-6 + 3x + -5x2 = -3x + 3x + 5x2 + -5x2

Combine like terms: -3x + 3x = 0
-6 + 3x + -5x2 = 0 + 5x2 + -5x2
-6 + 3x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6 + 3x + -5x2 = 0

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

Divide each side by '-5'.
1.2 + -0.6x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -0.6x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -0.6x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -0.6x + x2 = 0 + -1.2
-0.6x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-0.6x + x2 = -1.2

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = -1.2 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = -1.2 + 0.09

Combine like terms: -1.2 + 0.09 = -1.11
0.09 + -0.6x + x2 = -1.11

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = -1.11

Can't calculate square root of the right side.

The solution to this equation could not be determined.