(9x-y)^2-81x^2/7

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Solution for (9x-y)^2-81x^2/7 equation: 


x in (-oo:+oo)

(9*x-y)^2-((81*x^2)/7) = 0

(9*x-y)^2+(-81/7)*x^2 = 0

(9*x-y)^2+(-81*x^2)/7 = 0

(7*(9*x-y)^2)/7+(-81*x^2)/7 = 0

7*(9*x-y)^2-81*x^2 = 0

486*x^2-126*x*y+7*y^2 = 0

(486*x^2-126*x*y+7*y^2)/7 = 0

(486*x^2-126*x*y+7*y^2)/7 = 0 // * 7

486*x^2-126*x*y+7*y^2 = 0

486*x^2-126*x*y+7*y^2 = 0

DELTA = (-126*y)^2-(4*7*486*y^2)

DELTA = 2268*y^2

2268*y^2 = 0

2268*y^2 = 0 // : 2268

y^2 = 0

y = 0

DELTA = 0  <=>  t_3 = 0

x = (-(-126*y))/(2*486) i y = 0

x = (7*y)/54 i y = 0

( x = ((2268*y^2)^(1/2)-(-126*y))/(2*486) or x = (-(-126*y)-(2268*y^2)^(1/2))/(2*486) ) i y > 0

( x = (126*y+18*7^(1/2)*y)/972 or x = (126*y-18*7^(1/2)*y)/972 ) i y > 0

y+0 > 0

y > 0

y+0 > 0 // - 0

y > 0

x in { (7*y)/54, (126*y+18*7^(1/2)*y)/972, (126*y-18*7^(1/2)*y)/972 }

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