2 Added points of intersection edited Feb 6 '18 at 15:02 Bob Hanlon 65.5k33 gold badges3737 silver badges100100 bronze badges p = 1.6; α = 0.001; r = 0.6; η = 0.04; ω = 1; eqn = R ω p Sin[ω τ] + R ω p α - 9/4 r p R^3 ω - η p R == 0 // Rationalize // Simplify (* 3*R*(13 + 450*R^2) == 1000*R*Sin[τ] *)  The points of intersection are pts = {τ, R} /. SortBy[ Solve[#, {τ, R}][[1]] & /@ ({Reduce[ {eqn, eqn /. τ -> 20 - τ, 0 < τ < 20, 0 < R < 2}, {τ, R}] // Simplify // ToRules} /. Rule -> Equal), #[[1, -1]] &]  Which are approximately pts // N (* {{0.575222, 0.611629}, {6.85841, 0.611629}, {13.1416, 0.611629}, {19.4248, 0.611629}} *)  Plotting ContourPlot[ Evaluate@{eqn, eqn /. τ -> 20 - τ}, {τ, 0, 20}, {R, 0, 2}, ContourStyle -> {Blue, Green}, BaseStyle -> Thick, PlotLegends -> Placed["Expressions", {.5, .75}]]], Epilog -> {Red, AbsolutePointSize[5], Point[pts]}]  p = 1.6; α = 0.001; r = 0.6; η = 0.04; ω = 1; eqn = R ω p Sin[ω τ] + R ω p α - 9/4 r p R^3 ω - η p R == 0 // Rationalize // Simplify (* 3*R*(13 + 450*R^2) == 1000*R*Sin[τ] *) ContourPlot[ Evaluate@{eqn, eqn /. τ -> 20 - τ}, {τ, 0, 20}, {R, 0, 2}, ContourStyle -> {Blue, Green}, BaseStyle -> Thick, PlotLegends -> Placed["Expressions", {.5, .75}]]  p = 1.6; α = 0.001; r = 0.6; η = 0.04; ω = 1; eqn = R ω p Sin[ω τ] + R ω p α - 9/4 r p R^3 ω - η p R == 0 // Rationalize // Simplify (* 3*R*(13 + 450*R^2) == 1000*R*Sin[τ] *)  The points of intersection are pts = {τ, R} /. SortBy[ Solve[#, {τ, R}][[1]] & /@ ({Reduce[ {eqn, eqn /. τ -> 20 - τ, 0 < τ < 20, 0 < R < 2}, {τ, R}] // Simplify // ToRules} /. Rule -> Equal), #[[1, -1]] &]  Which are approximately pts // N (* {{0.575222, 0.611629}, {6.85841, 0.611629}, {13.1416, 0.611629}, {19.4248, 0.611629}} *)  Plotting ContourPlot[ Evaluate@{eqn, eqn /. τ -> 20 - τ}, {τ, 0, 20}, {R, 0, 2}, ContourStyle -> {Blue, Green}, BaseStyle -> Thick, PlotLegends -> Placed["Expressions", {.5, .75}], Epilog -> {Red, AbsolutePointSize[5], Point[pts]}]  1 answered Feb 6 '18 at 13:41 Bob Hanlon 65.5k33 gold badges3737 silver badges100100 bronze badges p = 1.6; α = 0.001; r = 0.6; η = 0.04; ω = 1; eqn = R ω p Sin[ω τ] + R ω p α - 9/4 r p R^3 ω - η p R == 0 // Rationalize // Simplify (* 3*R*(13 + 450*R^2) == 1000*R*Sin[τ] *) ContourPlot[ Evaluate@{eqn, eqn /. τ -> 20 - τ}, {τ, 0, 20}, {R, 0, 2}, ContourStyle -> {Blue, Green}, BaseStyle -> Thick, PlotLegends -> Placed["Expressions", {.5, .75}]]