The total cost of his session was $43.25. He had to pay a $7 entry fee and $1.25 every minute he was on the trampoline.

29 minutes

Step-by-step explanation:

You can set this up in a linear equation in slope-intercept form, where the y-intercept is the entry fee, y is the total cost, and the slope is the charge per minute. x will be the number of minutes he spent on the trampoline:

y=mx+b

43.25=1.25x+7

Then simplify:

36.25=1.25x

x=29

Therefore, he spent 29 minutes on the trampoline.

Since this does not factor you have to use the quadratic equation:
x= ( −b±√ b 2 −4ac )/2a
In this case your b=144 a=-16 and c=-80.  Make sure you keep the negative sign from the minus with the 80.  Then you plug in and do the math.
(-144±√(144)²-4(-16)(-80))/2(-16)
(-144±√20736-5120)/-32
(-144±√15616)/-32
(-144±16√61)/-32
So your two answers are:
x=(
x=

Hope that helps.  Let me know if any of that does not make sense.