140 + 10w = m
10w = $10 per week
140 = what he started with
It has no real solutions. To be precise, no real zeros (or roots).
The zeros (here called "solutions", I guess) are the points where the function intersects the x-axis: at those points the value of the function is zero. So they are solutions to the equation f(x)=0.
This function does not intersect the x-axis. Hence, no solutions.
The rate of change aka slope is -2