Examine whether the following equation is quadratic or not: $x(x+1)+8=(x+2)(x-2)$

Find the roots of the quadratic equation by using the quadratic formula:
$-3x^{2} + 5x + 12 = 0$

The golden number $\frac{1+\sqrt{5}}{2}$ is one of the solutions of ...... .

Find the roots of the quadratic equation $2x^{2}-\sqrt{5}x-2=0$ using the quadratic formula.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\sqrt{2} x^{2} + 7x + 5\sqrt{2} = 0$

Represent the following situation mathematically:
$A$ 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 ₹ $750$. We would like to find out the number of toys produced on that day.