Solve the following equation using the method of factorization: $x^{2} - 7 = 0$.

Find the discriminant of the following quadratic equation: $9x^{2} - bx + 3 = 0$.

Obtain the roots of the following equation using the method of 'completing the square': $3y^{2} + 7y - 20 = 0$.

Solve the following equation using the method of factorization: $6(2x+1)^2 - (2x+1) - 5 = 0$

Solve the following equation using the method of factorization: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6} \,(x \neq 3, -5)$

At $t$ minutes past $2\, pm$, the time needed by the minute hand of a clock to show $3\, pm$ was found to be $3\, minutes$ less than $\frac{t^{2}}{4}$ $minutes$. Find $t$.