The product of two consecutive positive integers is $306.$ Form the quadratic equation to find the integers, if $x$ denotes the smaller integer.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be $55$ minus the number of toys produced in a day. On a particular day, the total cost of production was $₹750$. If $x$ denotes the number of toys produced that day, form the quadratic equation fo find $x.$

(Note: The word article is replaced by toys)

Solve the following quadratic equations by factorization:

$(\mathrm{x}-4)(\mathrm{x}+2)=0$

Solve the quadratic equation $(2x+3)(3x-7)=0$ by factorization.

Solve the following quadratic equation by factorisation.

$3{\mathrm{x}}^2-14\mathrm{x}-5=0$