SOLUTION: 16t^2= 24t + 15 Solve for t

Algebra ->  Equations -> SOLUTION: 16t^2= 24t + 15 Solve for t      Log On


   

Question 292942: 16t^2= 24t + 15 Solve for t
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
16t%5E2=+24t+%2B+15 Start with the given equation.


16t%5E2-24t-15=0 Get everything to one side.


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for t:


Starting with the general quadratic


at%5E2%2Bbt%2Bc=0


the general solution using the quadratic equation is:


t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 16%2At%5E2-24%2At-15=0 ( notice a=16, b=-24, and c=-15)





t+=+%28--24+%2B-+sqrt%28+%28-24%29%5E2-4%2A16%2A-15+%29%29%2F%282%2A16%29 Plug in a=16, b=-24, and c=-15




t+=+%2824+%2B-+sqrt%28+%28-24%29%5E2-4%2A16%2A-15+%29%29%2F%282%2A16%29 Negate -24 to get 24




t+=+%2824+%2B-+sqrt%28+576-4%2A16%2A-15+%29%29%2F%282%2A16%29 Square -24 to get 576 (note: remember when you square -24, you must square the negative as well. This is because %28-24%29%5E2=-24%2A-24=576.)




t+=+%2824+%2B-+sqrt%28+576%2B960+%29%29%2F%282%2A16%29 Multiply -4%2A-15%2A16 to get 960




t+=+%2824+%2B-+sqrt%28+1536+%29%29%2F%282%2A16%29 Combine like terms in the radicand (everything under the square root)




t+=+%2824+%2B-+16%2Asqrt%286%29%29%2F%282%2A16%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




t+=+%2824+%2B-+16%2Asqrt%286%29%29%2F32 Multiply 2 and 16 to get 32


So now the expression breaks down into two parts


t+=+%2824+%2B+16%2Asqrt%286%29%29%2F32 or t+=+%2824+-+16%2Asqrt%286%29%29%2F32



Now break up the fraction



t=%2B24%2F32%2B16%2Asqrt%286%29%2F32 or t=%2B24%2F32-16%2Asqrt%286%29%2F32



Simplify



t=3%2F4%2Bsqrt%286%29%2F2 or t=3%2F4-sqrt%286%29%2F2



So the solutions are:

t=3%2F4%2Bsqrt%286%29%2F2 or t=3%2F4-sqrt%286%29%2F2