If xy*y + ty +z = 0,

Find y.

Originally posted by GinoJ
If xy*y + ty +z = 0,

Find y.

The quadratic formula suggests 2 solutions.

(-t - sqrt( t*t - 4*x*z)) / (2* x)
(-t + sqrt( t*t - 4*x*z)) / (2* x)

Derived by making a perfect square in order to remove the square function

x*y*y + t*y + z = 0
y*y + t*y/x + z/x = 0
y*y + t*y/x = -z/x
y*y + t*y/x + t*t/(4*x*x) = t*t/(4*x*x) - z/x
(y + t/(2*x))^2 = t*t/(4*x*x) - z/x
y + t/(2*x) = +- sqrt(t*t/(4*x*x) - z/x)
y + t/(2*x) = +- sqrt((t*t - 4*x*z)/(4*x*x))
y + t/(2*x) = 1/(2*x)*+- sqrt(t*t - 4*x*z)
y= -t/(2*x) +- sqrt(t*t - 4*x*z)/(2*x)
y= (-t +- sqrt(t*t - 4*x*z))/(2*x)

Originally posted by geepamoogle
The quadratic formula suggests 2 solutions.

(-t - sqrt( t*t - 4*x*z)) / (2* x)
(-t + sqrt( t*t - 4*x*z)) / (2* x)

Derived by making a perfect square in order to remove the square function

x*y*y + t*y + z = 0
y*y + t*y/x + z/x = 0
y*y + t*y/x = -z/x
y*y + t*y/x + t*t/(4*x*x) = t*t/(4*x*x) - z/x
(y + t/(2*x))^2 = t*t/(4*x*x) - z/x
y + t/(2*x ...[text shortened]... +- sqrt(t*t - 4*x*z)
y= -t/(2*x) +- sqrt(t*t - 4*x*z)/(2*x)
y= (-t +- sqrt(t*t - 4*x*z))/(2*x)

Originally posted by iraqi insurgent
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Originally posted by GinoJ
If xy*y + ty +z = 0,

Find y.