Solve the following equation by using the general formula,if the equation has a solution in $R$: $5x^{2} + 12x + 10 = 0$.

Solve the following equation using the method of 'completing the square': $4 x^{2}+3 x+5=0$

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 $t$.

Had Ajita scored $10$ more marks in her mathematics test out of $30$ marks,$9$ times these marks would have been the square of her actual marks. How many marks did she get in the test?

The value of the discriminant of a quadratic equation $kx^{2} - 4x - 4 = 0$ is $64$,then $k = \dots$

The product of the digits of a two-digit number is $15$. If the digits of this number are interchanged,the new number so obtained is $18$ more than the original number. Find the original number.