Posted by sam on .
solve by completeing the square
m^29/2m=3/2

algebra 
Henry,
m^2 9/2m = 3/2.
m^2 9/2m + (9/4)^2 = 3/2 + (9/4)^2
m^2  9/2m +(9/4)^2 = 24/16 + 81/16
m^2 9/2m + (9/4)^2 = 105/16
(m  9/4)^2 = 105/16
Take sqrt of both sides:
m  9/4 = (sqrt105)/4
m = 9/4 + (sqrt105)/4 = (9 + sqrt105)/4
m = 4.8, and 0.31.