Is x(x-6)=20 a quadratic equation

We can distribute the outer x to each term inside

x(x-6) = x^2-6x

So the original equation turns into

x^2-6x = 20

Then you could subtract 20 from both sides to get everything to the same side

x^2-6x-20 = 20-20

x^2-6x-20 = 0

This quadratic equation is in the form ax^2+bx+c = 0 with a = 1, b = -6, c = -20.

The presence of the x^2 term, and having it be the largest exponent, is what makes this a quadratic.