Question 1063679
.
{{{graph( 330, 330, -10.5, 10.5, -10.5, 10.5,
           -2x+3,  -2*3^x
)}}}


Plots y1 = -2x+3 (red) and  y2 = -2*3^x (green)


It looks like there are no solutions.


To prove it, consider the difference y3 = y1 - y2 = {{{(-2x+3) - (-2*3^x)}}} = {{{2*3^x-2x +3}}} and then find its minimum using differentiation. 
Then estimate this minimum and show that it is positive.


I didn't try it, but you can.