How to choose appropriate interval for secant method and integration

Question

I am given the following:

$\int e^{-2k(x-k)^2}/(2+k+x)=(4+k)/20$ , where the interval of the integral is $a=0$ and $b=3k$

Using the secant method and integration, I am asked to find all the solutions for $k$ ( where k>0) with at least 8 decimals.

For this I need an estimated interval of $k$ as well as a start value within that interval. How do I determine which interval of $k$ to set?

Thank you!

Edit

I tried to plot the function in Matlab but I am unsure how to write it, the code below is what how I thought it would be but it doesn't work. I want to be able to plot the function in Matlab and from that graph be able to determine my $k$-interval like the one from Wolfram Alpha.

F0 = [];
for k0 = [0:0.01:10];
x=0:0.1:3*k0;
y0 = @(x)((exp(-2*k0*(x-k0).^2))/(2+k0+x));
Int0=integral(y0,0,3*k0);
f0=Int0-((4+k0)/20);
F0 = [F0 f0];

end
plot(x,F0)

Answer 1

There are two solutions to this equation. One in the interval $[0,\frac 12]$ and another in the interval $[1, \frac 32]$. I got these intervals simply by plotting the function $f(k)=\int_0^{3k} \dfrac{e^{-2k(x-k)^2}}{2+k+x} dx-\frac{4+k}{20}$ (the integration was performed numerically).