Okay so, putting the numbers you are given into the equation you are given you have $4t+ (0.5)(4)t^2= 4t+ 2t^2= 250$ which is the same as $2t^2+ 4t- 250= 0$, a quadratic equation. You can solve that by "completing the square" or using the quadratic formula.
Completing the square, first divide each term by 2: $t^2+ 2t= 125$. Add 1 to both sides: $t^2+ 2t+ 1= (t+ 1)^2= 126$. Tale the square root of both sides: $t+ 1= \pm\sqrt{126}= \pm 3\sqrt{14}$. Finally, subtract 1 from both sides: $x= -1\pm 3\sqrt{14}$ seconds. I will leave it to you to decide which of the two roots is correct for this problem.