Solve the equation `15.2^(x+1)+15.2^(2-x)=135`

Explanation

This equation rewrite in the form
`30.2^x)+60/(2^(x))=135`
Let `t=2^(x)`
Then `30t^(2)-135t+60=0`
`implies6t^(2)-27t+12=0`
`implies6t^(2)-24t-3t+12=0`
`implies(t-4)(6t-3)=0`
Then `t_(1)=4` and `t_(2)=1/2`
Thus, given equation is equivalen to
`2^(x)=4` and `2^(x)=1/2`
Then `x_(1)=2` and `x_(2)=-1`
Hence roots of the original equation are `x_(1)=2` and `x_(2)=-1`.