At what time do two particles meet: factoring a polynomial.

[DavidAp]

Two particles move along the x-axis.
Particle one has the position x = 8t^2 + 7t + 2
Particle two has the acceleration a = -8t, and when t=0 v=23.
When the velocity of the particles match what is their velocity?



I thought of approaching this problem by changing both equations into the equations of velocity and setting them equal to each other to find the time in which their velocities match. Then I'll plug in the time into one of the two equations to find the velocity of when they meet.
---------------------------

Particle One:
8t^2 +7t +2 (d/dx) =
16t + 7 = v

----------------------------

Particle Two:
(integral) -8t =
-4t^2 + c = v

Since v=23 when t=0,
-4(0)^2 + c = 23
c = 23

So,
-4t^2 + 23 = v

---------------------------

Now when I set them equal to each other,
16t + 7 = -4t^2 + 23
4t^2 + 16t - 16 = 0
t^2 + 4t - 4

Now this is where I get stuck. I don't know how to solve this polynomial and therefore cannot find at what time the two particles have the same acceleration. Can somebody help me factor this! Am I not suppose to factor this, did I do something wrong?

Thanks in advance for taking the time to read my question.

 

[Pi-Bond]

Use the quadratic formula.

 

[DavidAp]

The quadratic formula? Wow, I forgot all about that...

*math math*

It works! Amazing! I feel so silly now for have asking this!
Thank you so much!