81*9^x-78*6^x+16*4^x=0

Question

81*9^x-78*6^x+16*4^x=0

Answer 1

81*3^2x -78*3^x*2^x+16*2^2x=0/4^2x
81*(3/2)^2x-78*(3/2)^x+16=0
(3/2)^x=a
81a²-78a+16=0
D=6084-5184=900
a1=(78-30)/162=48/162=8/27⇒(3/2)^x=(3/2)^-3⇒x=-3
a2=(78+30)/162=108/162=2/3⇒(3/2)^x=(3/2)^-1⇒x=-1