Let x be "the other" number.


Then "one number" is  (300-x).


From the condition, you have this equation

    300 - x = 2x^2.


The standard form is

    2x^2 + x - 300 = 0.


Solve it using the quadratic formula


     =  =  = 



You have two roots, -12.5  and  12.



They produce two solutions.



1)  One solution is this pair:    "one number" is 300-(-12.5) = 312.5; "the other number" is -12.5.


2)  Second solution is this pair: "one number is 12;                   "the other number" is (300-12) = 288.



CHECK.  1)  2x^2 = 2*(-12.5)^2 = 312.5.     ! correct !

        2)  2*12^2 = 288.                   ! correct !