The number happens to be the square root of 183.04=4576/25.
4576=4000+576=(20√10)^2+24^2; 4576/25=((20√10)^2+24^2)/5^2.
4576=(12√10)^2+56^2; 4576/25=((12/√10)^2+56^2)/5^2.
The first solution is the discriminant in the quadratic 5x^2+48x-800=0:
x=(-48±√(2304+16000)/10=(-24±√(576+4000))/5=(-24±√4576)/5=-24/5±√(4576/25)=-4.8±√183.04.
The second solution is the discriminant in the quadratic 5x^2+112x-288=0:
x=(-56±√4576)/5=-11.2±√183.04.