5y^2+13y=10

Solution for 5y^2+13y=10 equation:

Simplifying
5y2 + 13y = 10

Reorder the terms:
13y + 5y2 = 10

Solving
13y + 5y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + 13y + 5y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 13y + 5y2 = 0

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

Divide each side by '5'.
-2 + 2.6y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.6y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.6y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.6y + y2 = 0 + 2
2.6y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.6y + y2 = 2

The y term is 2.6y.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6y + 1.69 + y2 = 2 + 1.69

Reorder the terms:
1.69 + 2.6y + y2 = 2 + 1.69

Combine like terms: 2 + 1.69 = 3.69
1.69 + 2.6y + y2 = 3.69

Factor a perfect square on the left side:
(y + 1.3)(y + 1.3) = 3.69

Calculate the square root of the right side: 1.920937271

Break this problem into two subproblems by setting 
(y + 1.3) equal to 1.920937271 and -1.920937271.

Subproblem 1
y + 1.3 = 1.920937271

Simplifying
y + 1.3 = 1.920937271

Reorder the terms:
1.3 + y = 1.920937271

Solving
1.3 + y = 1.920937271

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-1.3' to each side of the equation.
1.3 + -1.3 + y = 1.920937271 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + y = 1.920937271 + -1.3
y = 1.920937271 + -1.3

Combine like terms: 1.920937271 + -1.3 = 0.620937271
y = 0.620937271

Simplifying
y = 0.620937271

Subproblem 2
y + 1.3 = -1.920937271

Simplifying
y + 1.3 = -1.920937271

Reorder the terms:
1.3 + y = -1.920937271

Solving
1.3 + y = -1.920937271

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-1.3' to each side of the equation.
1.3 + -1.3 + y = -1.920937271 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + y = -1.920937271 + -1.3
y = -1.920937271 + -1.3

Combine like terms: -1.920937271 + -1.3 = -3.220937271
y = -3.220937271

Simplifying
y = -3.220937271

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.620937271, -3.220937271}