7y^2-14y+3=0

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Solution for 7y^2-14y+3=0 equation:


Simplifying
7y2 + -14y + 3 = 0

Reorder the terms:
3 + -14y + 7y2 = 0

Solving
3 + -14y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
0.4285714286 + -2y + y2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -2y + -0.4285714286 + y2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + -2y + y2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + -2y + y2 = 0 + -0.4285714286
-2y + y2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
-2y + y2 = -0.4285714286

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = -0.4285714286 + 1

Reorder the terms:
1 + -2y + y2 = -0.4285714286 + 1

Combine like terms: -0.4285714286 + 1 = 0.5714285714
1 + -2y + y2 = 0.5714285714

Factor a perfect square on the left side:
(y + -1)(y + -1) = 0.5714285714

Calculate the square root of the right side: 0.755928946

Break this problem into two subproblems by setting 
(y + -1) equal to 0.755928946 and -0.755928946.

Subproblem 1

y + -1 = 0.755928946 Simplifying y + -1 = 0.755928946 Reorder the terms: -1 + y = 0.755928946 Solving -1 + y = 0.755928946 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 0.755928946 + 1 Combine like terms: -1 + 1 = 0 0 + y = 0.755928946 + 1 y = 0.755928946 + 1 Combine like terms: 0.755928946 + 1 = 1.755928946 y = 1.755928946 Simplifying y = 1.755928946

Subproblem 2

y + -1 = -0.755928946 Simplifying y + -1 = -0.755928946 Reorder the terms: -1 + y = -0.755928946 Solving -1 + y = -0.755928946 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -0.755928946 + 1 Combine like terms: -1 + 1 = 0 0 + y = -0.755928946 + 1 y = -0.755928946 + 1 Combine like terms: -0.755928946 + 1 = 0.244071054 y = 0.244071054 Simplifying y = 0.244071054

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.755928946, 0.244071054}

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