200=-5t^2+100t+15

Solution for 200=-5t^2+100t+15 equation:

200=-5t^2+100t+15

We move all terms to the left:

200-(-5t^2+100t+15)=0

We get rid of parentheses

5t^2-100t-15+200=0

We add all the numbers together, and all the variables

5t^2-100t+185=0

a = 5; b = -100; c = +185;
Δ = b2-4ac
Δ = -1002-4·5·185
Δ = 6300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6300}=\sqrt{900*7}=\sqrt{900}*\sqrt{7}=30\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-30\sqrt{7}}{2*5}=\frac{100-30\sqrt{7}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+30\sqrt{7}}{2*5}=\frac{100+30\sqrt{7}}{10}
$