Originally Posted by

**galactus** Just a quadratic.

$\displaystyle 200-40t=900(1-\frac{t}{5})^{2}$

$\displaystyle 200-4t=36t^{2}-360t+900$

$\displaystyle -36t^{2}+320t+700=>36t^{2}-3200t+747=>4(9t^{2}-80t+175)=>9t^{2}-80t+175=0$

Now, solve the quad. Use the quadratic formula. May be the best bet.

But you could factor.

Divide by 9 and rewrite:

$\displaystyle t^{2}-\frac{35}{9}t-5t+\frac{175}{9}$

$\displaystyle (t^{2}-\frac{35}{9}t)-(5t-\frac{175}{9})$

$\displaystyle t(t-\frac{35}{9})-5(t-\frac{35}{9})=0$

$\displaystyle \boxed{(t-5)(t-\frac{35}{9})=0}$