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# Quadratic Equations

Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth's orbit.

You went on a 360km train ride but you are late! If the train had just been 5 km/hr faster, then the train ride would have been one hour shorter.

How fast was the train going?

\[ x(x+1)(x+2)(x+3)=120\]

Find the sum of all the real roots of the equation above.

\[\large (x^2 - 5x + 5)^{(x^2 - 11x + 30)} = 1\]

How many different integers satisfy the equation above?

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