Can someone solve this equation for me please e5x068e10x0320

Can someone solve this equation for me please?

e^{5x}-0.68e^{-10x}-0.32=0

I know the answer is 0.1515 but I need the details!

Solution

e^{-5x}-0.68e^{-10x}-0.32=0

e^-5x -0.68e^(-10x) -0.32 =0

Let e^-5x = y

y - 0.68y^2 -0.32 = 0

Solve the quadratic equation:

The roots of the equation :

y = ( 0.68 + /- sqrt( 0.68^2 +4*0.32) )/2

y =1 , 0.470

Now e^-5x = y = 1

x = 0

e^-5x = 0.470

taking log on both sides:

-5x = ln(0.470)

x = 0.151

Solution : x=0 , 0.151