There appears to be a line length limit in WolframAlpha.

If I make changes like replacing (1/2)* with /2 and a_1 with a and a_2 with b and eliminate all non essential parens and spaces then I believe I get your expression down to

p*(a/(a+b)*d+((d/2-a/(a+b)*e)*b)/(a+b)-(d/2-b/(a+b)*e)*a/(a+b))+(1-p)*(d/2+delta) >= p/2*e+(1-p)*d/2

which appears to be under the line length limit.

When I enter that into WolframAlpha like this

WolframAlpha link

then it appears to give you a solution for p as desired.

For other problems which are more difficult to get under the line length limit it is sometimes possible with a little thought to divide a problem into two or more stages, use WolframAlpha to solve each step individually and combine the results into a final answer or computation.