600=-16t^2+200t+10

Solution for 600=-16t^2+200t+10 equation:

600=-16t^2+200t+10

We move all terms to the left:

600-(-16t^2+200t+10)=0

We get rid of parentheses

16t^2-200t-10+600=0

We add all the numbers together, and all the variables

16t^2-200t+590=0

a = 16; b = -200; c = +590;
Δ = b2-4ac
Δ = -2002-4·16·590
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-8\sqrt{35}}{2*16}=\frac{200-8\sqrt{35}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+8\sqrt{35}}{2*16}=\frac{200+8\sqrt{35}}{32}
$