How to solve for x? (2/9)x^2 + (4/3)x > 0.5^x

Hi all, for what I'm currently doing I need to find where that parabola is greater than the exponential equation.This may seem simple but I cant seem to do anything other than rephrase it without getting a solution. Any help appreciated. it seems as though the answer is where x>0 but I can't prove it algebraicly.
 

LCKurtz

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Hi all, for what I'm currently doing I need to find where that parabola is greater than the exponential equation.This may seem simple but I cant seem to do anything other than rephrase it without getting a solution. Any help appreciated. it seems as though the answer is where x>0 but I can't prove it algebraicly.
With over 300 posts, you should know by now not to put your equations in the title.

If you plot the functions on the two sides of the inequality you will see they cross near ##x=1/2##, not near ##x=0##. You can solve for it numerically.
 
Numerical analysis gives about 0.4, you are right. But is it undoable algebraicaly?
 
Thank you, like your signature by the way. "usual functions" is there an unusual one to do this job?
 

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