Question

Question #c3298

Answer 1

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.