Atheatre having 1200 seats all of wich are either balcony or ochrestra seat has 250 fewer balcony seats than orchestra seats how many balcony seats are there?

There are 475 balcony seats.

Step-by-step explanation:

Let be "b" the number of balcony seats in the theater and "o" the number of ochrestra seats in the theater.

Set up a system of equations:

Applying the Subsitution method, you can solve for "o" from the first equation:

 Now substitute this into the second one and solve for "b", in order to find its value:

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a