solve quadratic equation x^4– 13x^2= -3

let x^2 = t , then your equation becomes

t^2 - 13t + 3 = 0
t = (13 ± √157)/2
= (13 + √157)/2 or (13 - √157)/2

x = ± √[ (13 + √157)/2 ] or ±√[(1-√157)/2)

x = ± 3.573 or ± 0.485