Question #c3298

1 Answer
Jun 21, 2015

Answer:

This equation has no solutions.

Explanation:

First we can substitute #t=e^x#, this changes an exponential equation to a quadratic equation:

#t^2+8t+12=0#, but we only look for roots greater than zero, because #e^x# cannot be a negative number.

If we calculate #Delta# we find, that it is positive:

#Delta=8^2-4*1*12=64-48=16#

#sqrt(Delta)=4#

#t_1=(-8-4)/2=-6 <0#

#t_2=(-8+4)/2=-2<0#

The quadratc equation has 2 solutions, but neither of them is positive, so the base exponential equation has no solutions.