they are consecutive hence they can be written in this form x,x+1
product of the two rooms is 380380
x(x+1)=380380
[tex] {x}^{2} + x = 380380[/tex]
subtracting 380380 from both sides
[tex] {x}^{2} + x - 380380 = 0[/tex]
using the quadratic formula
[tex] \frac {- b + \sqrt{ {b}^{2} - 4ac} } {2a} [/tex]
[tex] \frac{ - 1 + \sqrt{1 - 4 \times 1 \times 380380} }{2 \times 1} [/tex]
x=616.2497 is room number1 x=617.2497 is room 2
but if you meant 380 instead of 380380
the equation will be
[tex] \frac{ - 1 + \sqrt{1 - 4 \times 1 \times - 380} }{2} [/tex]
the room numbers will exactly be 19,20
