I don't know why everyone is so keen on solving quadratic equations? It seems simpler to me to apply logs directly. For an example with changed values:
7^(3x)=4*7^x
=>
log_7(7^(3x)) = log_7(4*7^x)
=>
log_7(7^(3x)) = log_7(4) + log_7(7^x)
=>
3x = log_7(4) + x
=>
2x = log_7(4)
=>
x = log_7(4)/2