2y^2-3y+9=0

Solution for 2y^2-3y+9=0 equation:

Simplifying
2y2 + -3y + 9 = 0

Reorder the terms:
9 + -3y + 2y2 = 0

Solving
9 + -3y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
4.5 + -1.5y + y2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -1.5y + -4.5 + y2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -1.5y + y2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -1.5y + y2 = 0 + -4.5
-1.5y + y2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-1.5y + y2 = -4.5

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = -4.5 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = -4.5 + 0.5625

Combine like terms: -4.5 + 0.5625 = -3.9375
0.5625 + -1.5y + y2 = -3.9375

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = -3.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.