Question 48149
Solve fot t:

{{{rm = t^2-mt}}} You can use the quadratic formula or "complete the square" to solve this: Let's use the quadratic formula: {{{x=(-b+-sqrt(b^2-4ac))/2a}}}
First put your equation into the standard form:

{{{t^2-mt-mr = 0}}} Here, a = 1, b = -m, and c = -rm

{{{t = (-(-m)+-sqrt((-m)^2-4(1)(-rm)))/2(1)}}} It looks complicated but we can simplify it a bit.

{{{t=(m+-sqrt(m^2+4rm))/2}}} or, if you like:
{{{t = (m/2)+-sqrt(m^2+4rm)/2}}}