It's essential that you use " ^ " to indicate exponentiation if you want to communicate your ideas here accurately.
x2e5x + 3xe5x − e5x = 0 should be written as
x^2e^(5x) + 3xe^(5x) - 1e^(5x) = 0.
e^(5x) can be factored out of all four terms, leaving us with
e^(5x) [x^2 + 3x - 1] = 0. e^(5x) is never zero, so no solution there.
However, we can set x^2 + 3x - 1 equal to zero and solve for x:
-3 plus or minus sqrt(3^2 - 4(1)(-1) )
x = ----------------------------------------------------
2
-3 plus or minus sqrt(13)
= ----------------------------------------
2
So the original equation has two roots.
