14x^2-17xy+5y^2=0

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Solution for 14x^2-17xy+5y^2=0 equation: 


Simplifying
14x2 + -17xy + 5y2 = 0

Reorder the terms:
-17xy + 14x2 + 5y2 = 0

Solving
-17xy + 14x2 + 5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -5y)(2x + -1y) = 0


Subproblem 1
Set the factor '(7x + -5y)' equal to zero and attempt to solve:

Simplifying
7x + -5y = 0

Solving
7x + -5y = 0

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

Add '5y' to each side of the equation.
7x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
7x + 0 = 0 + 5y
7x = 0 + 5y
Remove the zero:
7x = 5y

Divide each side by '7'.
x = 0.7142857143y

Simplifying
x = 0.7142857143y

Subproblem 2
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {0.7142857143y, 0.5y}

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