2y^2+9y+42=0

Solution for 2y^2+9y+42=0 equation:

Simplifying
2y2 + 9y + 42 = 0

Reorder the terms:
42 + 9y + 2y2 = 0

Solving
42 + 9y + 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'.
21 + 4.5y + y2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 4.5y + -21 + y2 = 0 + -21

Reorder the terms:
21 + -21 + 4.5y + y2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 4.5y + y2 = 0 + -21
4.5y + y2 = 0 + -21

Combine like terms: 0 + -21 = -21
4.5y + y2 = -21

The y term is 4.5y.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5y + 5.0625 + y2 = -21 + 5.0625

Reorder the terms:
5.0625 + 4.5y + y2 = -21 + 5.0625

Combine like terms: -21 + 5.0625 = -15.9375
5.0625 + 4.5y + y2 = -15.9375

Factor a perfect square on the left side:
(y + 2.25)(y + 2.25) = -15.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.