Plot the real roots of an equation

Question

I wish to plot the real roots of the following equation as a graph of L versus r.

L^3 - L*b (P - r) == 0

with b=2.6666, P=10, for r in (1,100) with step size 0.1. I have tried the following which does not seem to work.

sol = Solve[L^3 - L*b (P - r) == 0, L];
With[{b = 2.6666, P = 10}, Plot[{f[L]}, {r, 1, 100, 0.1}]]

How can I plot L (y-axis) versus r (x-axis) for the given range of r?

Answer 1

Look at your function:

L^3 - L*b (P - r) == 0

One root will certainly be zero. That leaves a quadratic:

b = 2.6666;
P = 10;
sol = Solve[L^2 - b (P - r) == 0, L, Reals]

Therefore, there are only real roots for r<10:

Plot[L /. sol, {r, -5, 11}]

Answer 2

As @cvgmt alluded to in a comment, ContourPlot is great for such problems (especially when analytical solutions aren't available). In your case:

b = 2.6666; P = 10;
ContourPlot[L^3 - L*b (P - r) == 0, {r, -10, 20}, {L, -7, 7}, MaxRecursion -> 3]