There are two ways, completing the square
and quadratic formula.

COMPLETING THE SQUARE:
Get all variable terms on the left and
the constant term on the right:



Divide through by the coefficient of 





Multiply coefficient of t by :  =
Square that: 
Add 4/9 to both sides:



Factor left side, get LCD on the right:





Take square roots of both sides, remembering ± on the right







Add  to both sides:



Break up 76 by observing that it can
be divided by perfect square 4, so
76=4*19







So the two solutions are

 and 


==================================

QUADRATIC FORMULA

The solution to  is

 

with x=t, a=3, b=4, c=-24

  

 









Make two fractions:



Reduce the fractions by dividing top and bottom by 2:



So the two solutions are

 and 

Same answer.

Edwin