Algebra 2 question help. Need detailed answer.

Question

During the eruption of Mount St. Helens in 1980, debris was ejected at a speed of over 440 feet per second (300 miles per hour). The elevation in feet above sea level of a rock ejected at an angle of 75 degrees above horizontal is given by the function y(t) = -16t + 425t + 8200 where t is the time in seconds after the eruption. The rock's horizontal distance in feet from the point of ejection is given by x(t) = 113t. If the rock landed at an elevation of 6000 feet, what is the horizontal distance from the point of ejection to where it landed rounded to the nearest hundred feet?

Answer 1

6000 = 8200 + 425t - 16t²

The solution of the equation will give the time it takes for the rock to land at 6000 feet elevation.

Then 113 * the above solution will give the horizontal distance.

Please note there may well be an extraneous solution to the quadratic.

If you can't solve the quadratic, please let me know.