5h^2+20h+17=0

Solution for 5h^2+20h+17=0 equation:

Simplifying
5h2 + 20h + 17 = 0

Reorder the terms:
17 + 20h + 5h2 = 0

Solving
17 + 20h + 5h2 = 0

Solving for variable 'h'.

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

Divide each side by '5'.
3.4 + 4h + h2 = 0

Move the constant term to the right:

Add '-3.4' to each side of the equation.
3.4 + 4h + -3.4 + h2 = 0 + -3.4

Reorder the terms:
3.4 + -3.4 + 4h + h2 = 0 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
0.0 + 4h + h2 = 0 + -3.4
4h + h2 = 0 + -3.4

Combine like terms: 0 + -3.4 = -3.4
4h + h2 = -3.4

The h term is 4h.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4h + 4 + h2 = -3.4 + 4

Reorder the terms:
4 + 4h + h2 = -3.4 + 4

Combine like terms: -3.4 + 4 = 0.6
4 + 4h + h2 = 0.6

Factor a perfect square on the left side:
(h + 2)(h + 2) = 0.6

Calculate the square root of the right side: 0.774596669

Break this problem into two subproblems by setting 
(h + 2) equal to 0.774596669 and -0.774596669.

Subproblem 1
h + 2 = 0.774596669

Simplifying
h + 2 = 0.774596669

Reorder the terms:
2 + h = 0.774596669

Solving
2 + h = 0.774596669

Solving for variable 'h'.

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

Add '-2' to each side of the equation.
2 + -2 + h = 0.774596669 + -2

Combine like terms: 2 + -2 = 0
0 + h = 0.774596669 + -2
h = 0.774596669 + -2

Combine like terms: 0.774596669 + -2 = -1.225403331
h = -1.225403331

Simplifying
h = -1.225403331

Subproblem 2
h + 2 = -0.774596669

Simplifying
h + 2 = -0.774596669

Reorder the terms:
2 + h = -0.774596669

Solving
2 + h = -0.774596669

Solving for variable 'h'.

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

Add '-2' to each side of the equation.
2 + -2 + h = -0.774596669 + -2

Combine like terms: 2 + -2 = 0
0 + h = -0.774596669 + -2
h = -0.774596669 + -2

Combine like terms: -0.774596669 + -2 = -2.774596669
h = -2.774596669

Simplifying
h = -2.774596669

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {-1.225403331, -2.774596669}