Question 50571
-3y^2+6yt+5=0 
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You have a quadratic in y.  
Use the quadratic formula to get:
y=[-6t+-sqrt((6t)^2-4(-3)(5)]/-2*3
y=[-6t+-sqrt(36t+60)]/(-6)
y=[-6t+-2sqrt(9t+15)]/-6
y=[t+(1/3)sqrt(9t+15)]

Cheers,
Stan H.