6h^2=-5h+3

Solution for 6h^2=-5h+3 equation:

Simplifying
6h2 = -5h + 3

Reorder the terms:
6h2 = 3 + -5h

Solving
6h2 = 3 + -5h

Solving for variable 'h'.

Reorder the terms:
-3 + 5h + 6h2 = 3 + -5h + -3 + 5h

Reorder the terms:
-3 + 5h + 6h2 = 3 + -3 + -5h + 5h

Combine like terms: 3 + -3 = 0
-3 + 5h + 6h2 = 0 + -5h + 5h
-3 + 5h + 6h2 = -5h + 5h

Combine like terms: -5h + 5h = 0
-3 + 5h + 6h2 = 0

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

Divide each side by '6'.
-0.5 + 0.8333333333h + h2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.8333333333h + 0.5 + h2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.8333333333h + h2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.8333333333h + h2 = 0 + 0.5
0.8333333333h + h2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.8333333333h + h2 = 0.5

The h term is 0.8333333333h.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333h + 0.1736111111 + h2 = 0.5 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333h + h2 = 0.5 + 0.1736111111

Combine like terms: 0.5 + 0.1736111111 = 0.6736111111
0.1736111111 + 0.8333333333h + h2 = 0.6736111111

Factor a perfect square on the left side:
(h + 0.4166666667)(h + 0.4166666667) = 0.6736111111

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(h + 0.4166666667) equal to 0.82073815 and -0.82073815.

Subproblem 1
h + 0.4166666667 = 0.82073815

Simplifying
h + 0.4166666667 = 0.82073815

Reorder the terms:
0.4166666667 + h = 0.82073815

Solving
0.4166666667 + h = 0.82073815

Solving for variable 'h'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + h = 0.82073815 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + h = 0.82073815 + -0.4166666667
h = 0.82073815 + -0.4166666667

Combine like terms: 0.82073815 + -0.4166666667 = 0.4040714833
h = 0.4040714833

Simplifying
h = 0.4040714833

Subproblem 2
h + 0.4166666667 = -0.82073815

Simplifying
h + 0.4166666667 = -0.82073815

Reorder the terms:
0.4166666667 + h = -0.82073815

Solving
0.4166666667 + h = -0.82073815

Solving for variable 'h'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + h = -0.82073815 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + h = -0.82073815 + -0.4166666667
h = -0.82073815 + -0.4166666667

Combine like terms: -0.82073815 + -0.4166666667 = -1.2374048167
h = -1.2374048167

Simplifying
h = -1.2374048167

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.4040714833, -1.2374048167}