Solving Quadratics Equations? Math help please?

a)
t = 4.51528}

b)
t -> 1.87156

The pebble hits the ground when -5t^2 - 4t equals -120.

-5t^2 - 4t = -120

Rewrite into quadratic form:

-5t^2 - 4t + 120 = 0

Multiply through by -1 for convenience:

5t^2 + 4t - 120 = 0

Solve using the quadratic formula (or an online calculator like I did)

x = 4.52 (rounded) and x = -5.32 (rounded)

Ignore the negative root. It hits the ground in 4.52 seconds.

For the time to fall to 95 meters of height, use the equation:

-5t^2 - 4t = -25

In quadratic form:

5t^2 + 4t - 25 = 0

x = 1.87 (rounded) seconds

Ignore the -2.67 root.

h = -5t^2-4t+120
When the pebble hits the ground, h = 0
0 = -5t^2-4t+120
5t^2+4t - 120 = 0
And yes, it does not easily factor.
Use the Quadratic Formula
t = {-b +/-rt(b^2-4ac)} / 2a, where a=5, b= 4, c= -120

t = {-4+/-rt[(4)^2 -4(5)(-120)]} / 2(5)
t = {-4+/-rt[16+2400]} / 10
t = {-4 +/- rt [2416]} / 10
t = {-4 +/- 49.153} / 10
t = -53.153/10 or 45.153/10
t = -5.315 sec. or 4.515 sec.
Discard the negative answer for t
t= 4.515 sec.

Part 2 asks to find t when h = 95
95 = -t^2 -4t +120
t^2+4t - 25 = 0
Use the Quadratic Formula as before.
Here, a = 5, b=4, c=-25
I leave the work to you
Cheers!