find the Roots of this equation

Question

The roots of the equation $x^{4} -2x^{3} + x = 380$ are:

Though by trial and error one could solve the question, but I wanted to now if there is a particular method for solving the above equation ?

Answer 1

I got the answer

$x^4-2x^3+x^2-x^2+x-380=0$

$(x^2-x)^2-(x^2-x)-380=0$

$ p = x^2-x$

Now quadratic equation can be solved to get the answer

Answer 2

HINT: note that $$x^4-2x^3+x-380=\left( x+4 \right) \left( x-5 \right) \left( {x}^{2}-x+19 \right)$$