4y^2+5y=15

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Solution for 4y^2+5y=15 equation:


Simplifying
4y2 + 5y = 15

Reorder the terms:
5y + 4y2 = 15

Solving
5y + 4y2 = 15

Solving for variable 'y'.

Reorder the terms:
-15 + 5y + 4y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 5y + 4y2 = 0

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

Divide each side by '4'.
-3.75 + 1.25y + y2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 1.25y + 3.75 + y2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 1.25y + y2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 1.25y + y2 = 0 + 3.75
1.25y + y2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
1.25y + y2 = 3.75

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 = 3.75 + 0.390625

Reorder the terms:
0.390625 + 1.25y + y2 = 3.75 + 0.390625

Combine like terms: 3.75 + 0.390625 = 4.140625
0.390625 + 1.25y + y2 = 4.140625

Factor a perfect square on the left side:
(y + 0.625)(y + 0.625) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(y + 0.625) equal to 2.034852575 and -2.034852575.

Subproblem 1

y + 0.625 = 2.034852575 Simplifying y + 0.625 = 2.034852575 Reorder the terms: 0.625 + y = 2.034852575 Solving 0.625 + y = 2.034852575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = 2.034852575 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = 2.034852575 + -0.625 y = 2.034852575 + -0.625 Combine like terms: 2.034852575 + -0.625 = 1.409852575 y = 1.409852575 Simplifying y = 1.409852575

Subproblem 2

y + 0.625 = -2.034852575 Simplifying y + 0.625 = -2.034852575 Reorder the terms: 0.625 + y = -2.034852575 Solving 0.625 + y = -2.034852575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = -2.034852575 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = -2.034852575 + -0.625 y = -2.034852575 + -0.625 Combine like terms: -2.034852575 + -0.625 = -2.659852575 y = -2.659852575 Simplifying y = -2.659852575

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.409852575, -2.659852575}

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