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[kareolaussen]

Divide equation by 2^x, and define u = (5/2)^(x/2) to get equation
u^2 -1 = 2u or (u-1)^2 = 1+1 = 2.
u = 1 +√2 => x = 2*ln(1 + √2)/ln(5/2)=1.924.
u = 1 - √2 < 0 implies complex x.

[prollysine]

(5/2)^2x-6*(5/2)^x+1=0, let u=(5/2)^x, u^2-6u+1=0, u= 3+V8, 3-V8, x1=log(3+V8)/(5/2), x1=~ 1.92379,
x2=log(3-V8)/(5/2), x2=~ -1.92379, test x1, 5^x1-2^x1=~ 18.3199, 2*V(10*x1)=~ 18.3199, same, OK,
test x2, 5^x2-2^x2=~ -0.218342, , 2*V(10*x2)=~ 0.218342, not the same, false, solu, x=log(3+V8)/(5/2),