3 *5^(2x-1) -2*5^(x-1) = 0.2
3*5^2x* 5^(-1) - 2 *5^x * 5^(-1) - 0.2=0
3/5 * 5^2x - 2/5 * 5^x -0.2=0
5^x= t
3/5 t ² - 2/5 t - 0.2 =0
0.6t² - 0.4t -0.2=0 |:0,2
3t² - 2t - 1 =0
D= 4 - 4*3*(-1) = 4+12 = 16 = 4²
t₁= (2-4) / (2*3) = -2/6 = -1/3
t₂ = (2+4)/6 = 6/6 =1
5^x= - 1/3
5^x = - 3^(-1) - нет вещественных корней
5^x = 1
5^x = 5^0
x=0