5x^2+9y^2=14x^2-5y^2(6)

Solution for 5x^2+9y^2=14x^2-5y^2(6) equation:

Simplifying
5x2 + 9y2 = 14x2 + -5y2(6)

Reorder the terms for easier multiplication:
5x2 + 9y2 = 14x2 + -5 * 6y2

Multiply -5 * 6
5x2 + 9y2 = 14x2 + -30y2

Solving
5x2 + 9y2 = 14x2 + -30y2

Solving for variable 'x'.

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

Add '-14x2' to each side of the equation.
5x2 + -14x2 + 9y2 = 14x2 + -14x2 + -30y2

Combine like terms: 5x2 + -14x2 = -9x2
-9x2 + 9y2 = 14x2 + -14x2 + -30y2

Combine like terms: 14x2 + -14x2 = 0
-9x2 + 9y2 = 0 + -30y2
-9x2 + 9y2 = -30y2

Add '-9y2' to each side of the equation.
-9x2 + 9y2 + -9y2 = -30y2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
-9x2 + 0 = -30y2 + -9y2
-9x2 = -30y2 + -9y2

Combine like terms: -30y2 + -9y2 = -39y2
-9x2 = -39y2

Divide each side by '-9'.
x2 = 4.333333333y2

Simplifying
x2 = 4.333333333y2

Take the square root of each side:
x = {-2.081665999y, 2.081665999y}