Решение 

Уравнение равносильно системе:
Решим уравнение системы при помощи замены  

 

 

⇔ 

x = `+`(`*`(`/`(2, 3), `*`(arccos)), `*`(2, `*`(Pi, `*`(k)))), `in`(k, Z)
Image
Проверка: 

> solve(`+`(`*`(3, `*`(`^`(t, 2))), `-`(`*`(5, `*`(t))), 2) = 0)
 

1, `/`(2, 3) (5.2.1)
 

> solve(`/`(`*`(`+`(`*`(3, `*`(`^`(cos(x), 2))), `-`(`*`(5, `*`(cos(x)))), 2)), `*`(sqrt(sin(x)))) = 0)
 

arctan(`+`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2)))))), `+`(`-`(arctan(`+`(`*`(`/`(1, 2), `*`(`^`(5, `/`(1, 2)))))))) (5.2.2)
 

> with(plots); -1; `assign`(a1, polarplot(1, theta = 0 .. arccos(`/`(2, 3)), color = red, thickness = 10)); -1; `assign`(a2, polarplot(1, theta = `+`(`-`(arccos(`/`(2, 3)))) .. 0, color = blue, thicknes...
with(plots); -1; `assign`(a1, polarplot(1, theta = 0 .. arccos(`/`(2, 3)), color = red, thickness = 10)); -1; `assign`(a2, polarplot(1, theta = `+`(`-`(arccos(`/`(2, 3)))) .. 0, color = blue, thicknes...