4y^2+1=5y-3

Solution for 4y^2+1=5y-3 equation:

Simplifying
4y2 + 1 = 5y + -3

Reorder the terms:
1 + 4y2 = 5y + -3

Reorder the terms:
1 + 4y2 = -3 + 5y

Solving
1 + 4y2 = -3 + 5y

Solving for variable 'y'.

Reorder the terms:
1 + 3 + -5y + 4y2 = -3 + 5y + 3 + -5y

Combine like terms: 1 + 3 = 4
4 + -5y + 4y2 = -3 + 5y + 3 + -5y

Reorder the terms:
4 + -5y + 4y2 = -3 + 3 + 5y + -5y

Combine like terms: -3 + 3 = 0
4 + -5y + 4y2 = 0 + 5y + -5y
4 + -5y + 4y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
4 + -5y + 4y2 = 0

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

Divide each side by '4'.
1 + -1.25y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.25y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -1.25y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.25y + y2 = 0 + -1
-1.25y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.25y + y2 = -1

The y term is -1.25y.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25y + 0.390625 + y2 = -1 + 0.390625

Reorder the terms:
0.390625 + -1.25y + y2 = -1 + 0.390625

Combine like terms: -1 + 0.390625 = -0.609375
0.390625 + -1.25y + y2 = -0.609375

Factor a perfect square on the left side:
(y + -0.625)(y + -0.625) = -0.609375

Can't calculate square root of the right side.

The solution to this equation could not be determined.