SOLUTION: Solve for the ratio u:v if u^2 + 3uv - 10v^2 = 0

Divide both sides by v^2.  You will get

     = 0.    (1)


Introduce new variable  t = .

Then equation (1) takes the form

     = 0.


Factor left side

    (t+5)*(t-2) = 0.


The roots are   = - 5  and   = 2.


Hence,    = -5  or   = 2.    ANSWER

(u + 5v)(u - 2v) = 0

u + 5v = 0          OR            u - 2v = 0

u = - 5v            OR            u = 2v