Question 784773
{{{x}}}= number of M&M snacks the wizard had received
{{{6x}}}= 6 times the number of M&M snacks the wizard had received
{{{x-5}}}= five less than the number of M&M snacks the wizard received
{{{x^2}}}= the square of the number of M&M snacks the wizard received
 
What the wizard says in words, translates as
{{{6x/(x-5)=x^2}}}
To solve that equation, I would first multiply both sides of the equal sign times {{{(x-5)}}} to eliminate the denominator, and get
{{{6x=x^2(x-5)}}}
Then, it can be transformed and factored:
{{{6x=x^2(x-5)}}}-->{{{6x=x^3-5x^2}}}-->{{{x^3-5x^2-6x=0}}}-->{{{x(x^2-5x-6)=0}}}-->{{{x(x-6)(x+1)=0}}}
THe solutions to that equation are:
{{{x=-1}}} (which qould not make sense,
{{{x=0}}} (maybe the wizard did not get any M&M), and
{{{x=6}}}.

The wizard may have received 6 M&M's or none at all, but the witch, who got 7, had more M&M's.