Question 762392
Let A = number of teachers.
{{{1200/A = 1200/(A+2) + 20}}}
Multiply everything by A and (A+2)
{{{(1200/cross(A)) * cross(A) * (A+2) = (1200/cross((A+2)))*A*cross((A+2))+ 20*(A)*(A+2)}}}
Simplify the equation.
{{{1200*(A+2) = 1200A + 20A*(A+2)}}}
Multiply through.
{{{1200A + 2400 = 1200A + 20A^2 + 40A}}}
Subtract 1200A from both sides.
{{{2400 = 20A^2 + 40A}}}
Subtract 2400 from both sides.
{{{0 = 20A^2 + 40A - 2400}}}
I divide everything by 20 just to reduce the size of the numbers.
{{{0 = A^2 + 2A - 120}}}

Now use the quadratic equation to solve for X.
*[invoke quadratic "A", 1,2,-120]
A = 10 & -12
Since we can not have a negative number of people, A = 10
There were 10 teachers.