SOLUTION: I could really use some help on how to solve the following equation for t: {{{ h=-81t^2+at+c }}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I could really use some help on how to solve the following equation for t: {{{ h=-81t^2+at+c }}}       Log On


   

Question 706862: I could really use some help on how to solve the following equation for t:
+h=-81t%5E2%2Bat%2Bc+

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
That is an equation already solved for h. What are you looking for? It appears to be a quadratic equation with the variable, t. You can solve for t. You would treat just t as the only variable, and put the equation into the typical, "=0" form, and use general solution for a quadratic equation:

+h=-81t%5E2%2Bat%2Bc+
-81t%5E2%2Bat%2Bc-h=0
-81t%5E2%2Bat%2B%28c-h%29=0

Your solutions for t are these:
t=%28-a%2Bsqrt%28a%5E2-4%2A%28-81%29%2A%28c-h%29%29%29%2F%282%28-81%29%29
OR
t=%28-a-sqrt%28a%5E2-4%2A%28-81%29%2A%28c-h%29%29%29%2F%282%28-81%29%29

You might then take, for example the "+" form, as the simpler looking:
%28-a%2Bsqrt%28a%5E2%2B324%28c-h%29%29%29%2F%28-162%29
and the "-" form, as:
%28-a-sqrt%28a%5E2%2B324%28c-h%29%29%29%2F%28-162%29