15(x^2+y^2)=289(x^2-y^2)

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Solution for 15(x^2+y^2)=289(x^2-y^2) equation: 


Simplifying
15(x2 + y2) = 289(x2 + -1y2)
(x2 * 15 + y2 * 15) = 289(x2 + -1y2)
(15x2 + 15y2) = 289(x2 + -1y2)
15x2 + 15y2 = (x2 * 289 + -1y2 * 289)
15x2 + 15y2 = (289x2 + -289y2)

Solving
15x2 + 15y2 = 289x2 + -289y2

Solving for variable 'x'.

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

Add '-289x2' to each side of the equation.
15x2 + -289x2 + 15y2 = 289x2 + -289x2 + -289y2

Combine like terms: 15x2 + -289x2 = -274x2
-274x2 + 15y2 = 289x2 + -289x2 + -289y2

Combine like terms: 289x2 + -289x2 = 0
-274x2 + 15y2 = 0 + -289y2
-274x2 + 15y2 = -289y2

Add '-15y2' to each side of the equation.
-274x2 + 15y2 + -15y2 = -289y2 + -15y2

Combine like terms: 15y2 + -15y2 = 0
-274x2 + 0 = -289y2 + -15y2
-274x2 = -289y2 + -15y2

Combine like terms: -289y2 + -15y2 = -304y2
-274x2 = -304y2

Divide each side by '-274'.
x2 = 1.109489051y2

Simplifying
x2 = 1.109489051y2

Take the square root of each side:
x = {-1.053322862y, 1.053322862y}

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