The sum of two natural numbers is $8$ and the difference of their reciprocals is $\frac{2}{15}$. Find the numbers.

Solve the following and calculate the answer correct to two decimal places.

$x^2-5x-10=0$

Without solving the following quadratic equation, find the value of $p$ for which the given equation has real and equal roots.

$x^2+(p-3)x+p=0$

Solve the following equation and give your answer correct to three significant figures. 

$5x^2-3x-4=0$

Without solving the following quadratic equation, find the value of $m$ for which the given equation has real and equal roots.

${\mathrm{x}}^2+2(\mathrm{m}-1)\mathrm{x}+(\mathrm{m}+5)=0$

A car covers a distance of $400 km$ at a certain speed. Had the speed been$12 km/h$ more, the time taken for the journey would have been$1 h 40 min$ less. Find the original speed of the car in $km/hr$.