Solve in $\mathbb{R}$ the equation : $x^4+x-4=0$

Question

How do I solve, in $\mathbb{R}$, the following equation : $x^4+x-4=0$. I used the function $f(x)=x^4+x-4$ to prove that it has exactly two solutions; one less than, and the other great than $-\sqrt[3]{\dfrac{1}{4}}$. But I don't know how to find the solutions.

Answer 1

Since this isn't factorable, you could graph it and then find the zeroes / x-intercepts. Using desmos, I got x = -1.534 and x = 1.284.