hello :
25 = 5²
25^x = ( 5² ) ^x = (5^x)²
let : 5^x = t ..... t > 0
the equation : 2(25^x) = 3 - 5^x equiv :
2t² =3 -t and : 5^x = t ..... t > 0
2t² +t -3 =0
the discriminant : Δ = b² -4ac = (1)² -4(2)(-3) = 25 = 5²
t1 = (-1-5)/4 ( refused : t > 0 )
t2 = (-1+5)/4 =1
but: 5^x = t
5^x = 1
the solution is : x=0
