Question 1923
easy...do not be scared of inequalities.

Solve {{{x^2-5x-7=0}}}

You cannot factorise this, so use the formula..see my recent answers on this method.

Answers here are {{{x = (5+sqrt(53))/(2)}}} and {{{x = (5-sqrt(53))/(2)}}}. These are called the roots of the equation. Note the "5+" answer is a bigger number than the "5-" number.

Now, any +x^2 graph is u-shaped and I have just found where it crosses the x-axis, so where will the curve have negative values? Well, any x value between these 2 root values (just sketch a u-shaped curve that cuts the x-axis to see what i mean, so this is your inequality answer.

{{{(5-sqrt(53))/(2)}}} < x < {{{(5+sqrt(53))/(2)}}}

Hope this makes sense.

cheers
Jon.