Examine whether the following equation is quadratic or not: $(x-2)^{2}+1=2x-3$.

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $y^{2}+10y+6=0$

In quadratic equation $ax^{2} + bx + c = 0$,where $a \neq 0$,$b = 0$,and $D > 0$,then both the roots of the equation are .....

When there is a decrease of $5\, km/hr$ in the usual uniform speed of a train,it takes $4$ hours more than the usual time for covering the distance of $400\, km$. Find the usual speed of the train.

Find the roots of the quadratic equation by using the quadratic formula: $-x^{2}+7x-10=0$.

The length of the hypotenuse of an isosceles right-angled triangle is $8 \, cm$. Find the length of the other two sides.