I've made a procedure to fin the real roots of 2x³-4x²-22x+24, my result gives me:

2x³+(-4x²)+(-22x)+(24) has three real roots:

2/337^1/2sin(1/6Pi+1/3arccos(55/1369*37^1/2))+2/3,

-1/337^1/2(sin(1/6Pi+1/3arccos(55/136937^1/2))+3^1/2sin(1/3Pi-1/3arccos(55/1369*37^1/2)))+2/3,

-1/337^1/2(sin(1/6