What is the answer to this equation?

M = 10.86(D-t)t

First, substitute the values you have for M and D in the equation to get:

10.82 = 10.86(16-t)t

Multiply out the bracket to get:

10.83 = 173.76t - 10.86t^2

Note, the t^2 means t squared. Now rearrange the equation to get:

10.86t^2 - 173.76t + 10.83 = 0

This one of the old infamous quadratic equations (and a nasty one at that!) and is solved using the quadratic formula

t = {-b +or- sq.root[b^2 - 4ac]}/2a

where a = 10.86, b = -173.76 and c = 10.83

What follows will look pretty horrific after 15 years but you have to calculate:

{-(-173.76) + or - [(-173.76)^2 - 4x10.86x10.83)] /2 x 10.86

You will get:

t = 15.937 and t = 0.063

Don't be surprised that you get two answers.

Hope this has helped, saved your job and got you a pay rise.

do you have M and D as actual numbers? that would be easier, if not:

M = 10.86(D-t)t

M = 10.86Dt - 10.86t^2

10.86t^2 - 10.86Dt + M = 0

then use the quadratic formula

a = 10.86

b = -10.86D

c = M

t = (-b +/- sqrt(b^2 - 4ac)) / 2a

t = (-(-10.86D) +/- sqrt((-10.86D)^2 - 4(10.86)(M)) / 2(10.86)

t = (10.86D +/- sqrt(117.94D^2-43.44M)) / 21.72

Edit:

M is 70.82 and D is 16.

t = (10.86(16) +/- sqrt(117.94(16)^2-43.44(70.82))) / 21.72

t = (173.76 +/- sqrt(30192.64-3076.42)) / 21.72

t = (173.76 +/- sqrt(27116.22)) / 21.72

t = (173.76 +/- 164.67) / 21.72

either t = 173.76+164.67/21.72 = 15.5814788

or t = 173.76-164.67/21.72 = 0.4185211

if you put those into your trial and error spreadsheet they should come out, you can do it by trial and error, but that can take forever sometimes!!

write in quadratic form, At^2 + Bt + C = 0, then use the quadratic formula, t = [ -B+- sqrt(B^2-4AC) ] / 2a

Here, the quadratic form is:

-10.86t^2 + 10.86Dt - M = 0

So we have: A = -10.86, B = 10.86D, C = -M

Plug these in the quadratic formula and you'll get your answer!