The roots of a quadratic equation $(x-7)^{2}-16=0$ are ...... .

The faster train takes $1$ hour less than the slower train for covering a $400\, km$ distance. If the speed of the slower train is $20\, km/hr$ less than the speed of the faster train,find the speed of the slower train.

Find whether the following equation has real roots. If real roots exist,find them.
$5x^{2}-2x-10=0$

State whether the quadratic equation $(x-1)(x+2)+2=0$ has two distinct real roots. Justify your answer.

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Find the roots of the following quadratic equation by the method of completing the square: $3 y^{2}+7 y-20=0$