how do i solve: 200 = 1.862t^2 - 50t - 2

just as you would any quadratic:

1.862t^2 - 50t - 2 = 200
1.862t^2 - 50t - 202 = 0

t = (50±√(50^2 - 4(1.862)(-202)))/(2*1.862)
= (50±√4004.496)/3.722
= (50±63.281)/3.722
= -3.566 or 30.419