Question 1056543
Let {{{ x }}} = her brother's age
{{{ x - 6 }}} = the girl's age
-------------------------------
{{{ x*( x - 6 ) = 135 }}}
{{{ x^2 - 6x = 135 }}}
I will solve by completing the square
{{{ x^2 - 6x + (-6/2)^2 = 135 + (-6/2)^2 }}}
{{{ x^2 - 6x + 9 = 135 + 9 }}}
{{{ ( x - 3 )^2 = 144 }}}
{{{ ( x - 3 )^2 = 12^2 }}}
{{{ x - 3 = 12 }}}
{{{ x = 15 }}}
There is another root you get by taking the 
negative square root of {{{ 12^2 = -12 }}},
but ages can't be negative
also:
{{{ x - 6 = 9 }}}
---------------------
The brother is 15
The girl is 9
---------------------
check:
{{{ x*( x - 6 ) = 135 }}}
{{{ 15*9 = 135 }}}
{{{ 135 = 135 }}}
OK