t=-16t^2+600t+4

Solution for t=-16t^2+600t+4 equation:

t=-16t^2+600t+4

We move all terms to the left:

t-(-16t^2+600t+4)=0

We get rid of parentheses

16t^2-600t+t-4=0

We add all the numbers together, and all the variables

16t^2-599t-4=0

a = 16; b = -599; c = -4;
Δ = b2-4ac
Δ = -5992-4·16·(-4)
Δ = 359057
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-599)-\sqrt{359057}}{2*16}=\frac{599-\sqrt{359057}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-599)+\sqrt{359057}}{2*16}=\frac{599+\sqrt{359057}}{32}
$