Find the value of $x$ for which $x$ degrees Fahrenheit is exactly the same as $x$ degrees Celsius (remember the formula for converting Celsi

F = (9/5)C  + 32   (1)     

C = (F - 32)(5/9)   (2)       ....so.....setting (1) = (2), we have

(9/5)C + 32  = (F- 32)(5/9)      multiply both sides by  (9/5)

(81/25)C  + 288/5  = F - 32     add 32 to both sides

(81/25)C + 288/5 + 32  = F

(81/25)C + 448/5 = F    (3)       and putting (3) into (1), we have

(81/25)C + 448/5  =  (9/5)C  + 32     simplify

(81/25)C - (9/5)C  =  32 - 448/5      ......     (9/5) = (45/25)   and  32  = 160/5

(36/25)C  = [160 - 448]/5

(36/25)C  = [-288/5]    

(36/25)C = -1440/25       multiply through by 25

36C  = -1440       divide both sides by 36

C = -40      and F = (9/5)(-40) + 32  =  -72 + 32 =  -40

So....they are equal at -40