3*4^х+2*9^х=5*6^х найти х

3*4^х+2*9^х=5*6^х

3*4^х+2*9^х - 5*6^х=0 / 9^х

3 (4/9) ˣ + 2 - 5 (6/9) ˣ = 0

3 (2/3) ²ˣ - 5 (2/3) ˣ + 2=0 (2/3) ˣ=a a>0

3a² - 5a+2=0

D=25+24=1

a₁ = (5+1) / 6=1 (2/3) ˣ=1 x₁=0

a₂ = (5-1) / 6=2/3 (2/3) ˣ = 2/3 x₂=1