Finding maximum allowable alternating stress using goodmans relation

[mammal]

Homework Statement

(b) A steel alloy has an ultimate tensile strength of 820MN/m2 and a fatigue endurance limit of 390MN/m2. The steel is used in a fatigue application in which the alternating stress is 0.3 times the mean stress. Using the Goodman method with a factor of safety of 1.5 applied determine the maximum allowable alternating stress that will allow safe operation

Homework Equations

σa = σfat x (σm/σts)
Where σa is the alternating stress, σm is the mean stress, σfat is the fatigue endurance limit and σts is the ultimate tensile stress.

The Attempt at a Solution

So far I have substituted σa for 0.3 x σm and tried to rearrange this formula, I have however run into problems and am doubting this is the correct method.

 

[mammal]

Any ideas? The entire assignment is due in on monday and this is all I'm having problems with.