5y^2=6y-3

Solution for 5y^2=6y-3 equation:

Simplifying
5y2 = 6y + -3

Reorder the terms:
5y2 = -3 + 6y

Solving
5y2 = -3 + 6y

Solving for variable 'y'.

Reorder the terms:
3 + -6y + 5y2 = -3 + 6y + 3 + -6y

Reorder the terms:
3 + -6y + 5y2 = -3 + 3 + 6y + -6y

Combine like terms: -3 + 3 = 0
3 + -6y + 5y2 = 0 + 6y + -6y
3 + -6y + 5y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
3 + -6y + 5y2 = 0

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

Divide each side by '5'.
0.6 + -1.2y + y2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.2y + -0.6 + y2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.2y + y2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.2y + y2 = 0 + -0.6
-1.2y + y2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-1.2y + y2 = -0.6

The y term is -1.2y.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2y + 0.36 + y2 = -0.6 + 0.36

Reorder the terms:
0.36 + -1.2y + y2 = -0.6 + 0.36

Combine like terms: -0.6 + 0.36 = -0.24
0.36 + -1.2y + y2 = -0.24

Factor a perfect square on the left side:
(y + -0.6)(y + -0.6) = -0.24

Can't calculate square root of the right side.

The solution to this equation could not be determined.