5a^2-12a+6=0

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Solution for 5a^2-12a+6=0 equation:


Simplifying
5a2 + -12a + 6 = 0

Reorder the terms:
6 + -12a + 5a2 = 0

Solving
6 + -12a + 5a2 = 0

Solving for variable 'a'.

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

Divide each side by '5'.
1.2 + -2.4a + a2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -2.4a + -1.2 + a2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -2.4a + a2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -2.4a + a2 = 0 + -1.2
-2.4a + a2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-2.4a + a2 = -1.2

The a term is -2.4a.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4a + 1.44 + a2 = -1.2 + 1.44

Reorder the terms:
1.44 + -2.4a + a2 = -1.2 + 1.44

Combine like terms: -1.2 + 1.44 = 0.24
1.44 + -2.4a + a2 = 0.24

Factor a perfect square on the left side:
(a + -1.2)(a + -1.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(a + -1.2) equal to 0.489897949 and -0.489897949.

Subproblem 1

a + -1.2 = 0.489897949 Simplifying a + -1.2 = 0.489897949 Reorder the terms: -1.2 + a = 0.489897949 Solving -1.2 + a = 0.489897949 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + a = 0.489897949 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + a = 0.489897949 + 1.2 a = 0.489897949 + 1.2 Combine like terms: 0.489897949 + 1.2 = 1.689897949 a = 1.689897949 Simplifying a = 1.689897949

Subproblem 2

a + -1.2 = -0.489897949 Simplifying a + -1.2 = -0.489897949 Reorder the terms: -1.2 + a = -0.489897949 Solving -1.2 + a = -0.489897949 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + a = -0.489897949 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + a = -0.489897949 + 1.2 a = -0.489897949 + 1.2 Combine like terms: -0.489897949 + 1.2 = 0.710102051 a = 0.710102051 Simplifying a = 0.710102051

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.689897949, 0.710102051}

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